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This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers.
gauge multivalued integral --- scalarly defined multivalued integral --- decomposition of a multifunction --- Kuelbs–Steadman space --- Henstock–Kurzweil integrable function --- vector measure --- dense embedding --- completely continuous embedding --- Köthe space --- Banach lattice --- fractional differential inclusion --- maximal monotone operator --- Riemann–Liouville integral --- absolutely continuous in variation --- Vladimirov pseudo-distance --- fuzzy measure space --- fuzzy integration --- t-norm --- Chebyshev’s inequality --- Hölder’s inequality --- periodic boundary value inclusion --- Stieltjes derivative --- Stieltjes integrals --- Bohnenblust–Karlin fixed-point theorem --- regulated function --- solution set --- discontinuous function --- impulsive problem with variable times --- Riemann-Lebesgue integral --- interval valued (set) multifunction --- non-additive set function --- image processing --- b-metric space --- Hβ-Hausdorff–Pompeiu b-metric --- multi-valued fractal --- iterated multifunction system --- integral inclusion
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The description for this book, Contributions to Fourier Analysis. (AM-25), will be forthcoming.
Fourier analysis. --- Analysis, Fourier --- Mathematical analysis --- Absolute value. --- Almost periodic function. --- Approximation. --- Bessel function. --- Bilinear map. --- Boundary value problem. --- Characterization (mathematics). --- Coefficient. --- Compact space. --- Comparison theorem. --- Conservative vector field. --- Constant function. --- Continuous function. --- Corollary. --- Counterexample. --- Diagonalization. --- Diagram (category theory). --- Diameter. --- Dimension. --- Dirichlet kernel. --- Dirichlet problem. --- Dirichlet's principle. --- Distribution function. --- Exponential polynomial. --- Exponential sum. --- Fourier series. --- Fourier transform. --- Harmonic function. --- Hilbert space. --- Hölder's inequality. --- Integer. --- Interpolation theorem. --- Linear combination. --- Lp space. --- Measurable function. --- Measure (mathematics). --- Partial derivative. --- Partial differential equation. --- Periodic function. --- Poisson formula. --- Polynomial. --- Power series. --- Quantity. --- Rectangle. --- Remainder. --- Semicircle. --- Several complex variables. --- Sign (mathematics). --- Simple function. --- Special case. --- Sphere. --- Square root. --- Step function. --- Subsequence. --- Subset. --- Theorem. --- Theory. --- Triangle inequality. --- Two-dimensional space. --- Uniform continuity. --- Uniform convergence. --- Variable (mathematics). --- Vector field. --- Vector space.
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This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers.
Research & information: general --- Mathematics & science --- gauge multivalued integral --- scalarly defined multivalued integral --- decomposition of a multifunction --- Kuelbs–Steadman space --- Henstock–Kurzweil integrable function --- vector measure --- dense embedding --- completely continuous embedding --- Köthe space --- Banach lattice --- fractional differential inclusion --- maximal monotone operator --- Riemann–Liouville integral --- absolutely continuous in variation --- Vladimirov pseudo-distance --- fuzzy measure space --- fuzzy integration --- t-norm --- Chebyshev’s inequality --- Hölder’s inequality --- periodic boundary value inclusion --- Stieltjes derivative --- Stieltjes integrals --- Bohnenblust–Karlin fixed-point theorem --- regulated function --- solution set --- discontinuous function --- impulsive problem with variable times --- Riemann-Lebesgue integral --- interval valued (set) multifunction --- non-additive set function --- image processing --- b-metric space --- Hβ-Hausdorff–Pompeiu b-metric --- multi-valued fractal --- iterated multifunction system --- integral inclusion
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This Special Issue contains eight original papers with a high impact in various domains of set-valued analysis. Set-valued analysis has made remarkable progress in the last 70 years, enriching itself continuously with new concepts, important results, and special applications. Different problems arising in the theory of control, economics, game theory, decision making, nonlinear programming, biomathematics, and statistics have strengthened the theoretical base and the specific techniques of set-valued analysis. The consistency of its theoretical approach and the multitude of its applications have transformed set-valued analysis into a reference field of modern mathematics, which attracts an impressive number of researchers.
Research & information: general --- Mathematics & science --- gauge multivalued integral --- scalarly defined multivalued integral --- decomposition of a multifunction --- Kuelbs–Steadman space --- Henstock–Kurzweil integrable function --- vector measure --- dense embedding --- completely continuous embedding --- Köthe space --- Banach lattice --- fractional differential inclusion --- maximal monotone operator --- Riemann–Liouville integral --- absolutely continuous in variation --- Vladimirov pseudo-distance --- fuzzy measure space --- fuzzy integration --- t-norm --- Chebyshev’s inequality --- Hölder’s inequality --- periodic boundary value inclusion --- Stieltjes derivative --- Stieltjes integrals --- Bohnenblust–Karlin fixed-point theorem --- regulated function --- solution set --- discontinuous function --- impulsive problem with variable times --- Riemann-Lebesgue integral --- interval valued (set) multifunction --- non-additive set function --- image processing --- b-metric space --- Hβ-Hausdorff–Pompeiu b-metric --- multi-valued fractal --- iterated multifunction system --- integral inclusion
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This book contains an exposition of some of the main developments of the last twenty years in the following areas of harmonic analysis: singular integral and pseudo-differential operators, the theory of Hardy spaces, Lsup estimates involving oscillatory integrals and Fourier integral operators, relations of curvature to maximal inequalities, and connections with analysis on the Heisenberg group.
Harmonic analysis. Fourier analysis --- Harmonic analysis --- Analyse harmonique --- Harmonic analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Groupe de Heisenberg. --- Addition. --- Analytic function. --- Asymptote. --- Asymptotic analysis. --- Asymptotic expansion. --- Asymptotic formula. --- Automorphism. --- Axiom. --- Banach space. --- Bessel function. --- Big O notation. --- Bilinear form. --- Borel measure. --- Boundary value problem. --- Bounded function. --- Bounded mean oscillation. --- Bounded operator. --- Boundedness. --- Cancellation property. --- Cauchy's integral theorem. --- Cauchy–Riemann equations. --- Characteristic polynomial. --- Characterization (mathematics). --- Commutative property. --- Commutator. --- Complex analysis. --- Convolution. --- Differential equation. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Dirac delta function. --- Dirichlet problem. --- Elliptic operator. --- Existential quantification. --- Fatou's theorem. --- Fourier analysis. --- Fourier integral operator. --- Fourier inversion theorem. --- Fourier series. --- Fourier transform. --- Fubini's theorem. --- Function (mathematics). --- Fundamental solution. --- Gaussian curvature. --- Hardy space. --- Harmonic function. --- Heisenberg group. --- Hilbert space. --- Hilbert transform. --- Holomorphic function. --- Hölder's inequality. --- Infimum and supremum. --- Integral transform. --- Interpolation theorem. --- Lagrangian (field theory). --- Laplace's equation. --- Lebesgue measure. --- Lie algebra. --- Line segment. --- Linear map. --- Lipschitz continuity. --- Locally integrable function. --- Marcinkiewicz interpolation theorem. --- Martingale (probability theory). --- Mathematical induction. --- Maximal function. --- Meromorphic function. --- Multiplication operator. --- Nilpotent Lie algebra. --- Norm (mathematics). --- Number theory. --- Operator theory. --- Order of integration (calculus). --- Orthogonality. --- Oscillatory integral. --- Poisson summation formula. --- Projection (linear algebra). --- Pseudo-differential operator. --- Pseudoconvexity. --- Rectangle. --- Riesz transform. --- Several complex variables. --- Sign (mathematics). --- Singular integral. --- Sobolev space. --- Special case. --- Spectral theory. --- Square (algebra). --- Stochastic differential equation. --- Subharmonic function. --- Submanifold. --- Summation. --- Support (mathematics). --- Theorem. --- Translational symmetry. --- Uniqueness theorem. --- Variable (mathematics). --- Vector field. --- Fourier, Analyse de --- Fourier, Opérateurs intégraux de
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The description for this book, Multiple Integrals in the Calculus of Variations and Nonlinear Elliptic Systems. (AM-105), Volume 105, will be forthcoming.
Calculus of variations --- Integrals, Multiple --- Differential equations, Elliptic --- Calcul des variations --- Equations différentielles elliptiques --- $ PDMC --- Multiple integrals --- Calculus of variations. --- Multiple integrals. --- Differential equations, Elliptic. --- Equations différentielles elliptiques --- Elliptic differential equations --- Elliptic partial differential equations --- Linear elliptic differential equations --- Differential equations, Linear --- Differential equations, Partial --- Double integrals --- Iterated integrals --- Triple integrals --- Integrals --- Probabilities --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- A priori estimate. --- Analytic function. --- Boundary value problem. --- Coefficient. --- Compact space. --- Convex function. --- Convex set. --- Corollary. --- Counterexample. --- David Hilbert. --- Dense set. --- Derivative. --- Differentiable function. --- Differential geometry. --- Dirichlet integral. --- Dirichlet problem. --- Division by zero. --- Ellipse. --- Energy functional. --- Equation. --- Estimation. --- Euler equations (fluid dynamics). --- Existential quantification. --- First variation. --- Generic property. --- Harmonic function. --- Harmonic map. --- Hausdorff dimension. --- Hölder's inequality. --- I0. --- Infimum and supremum. --- Limit superior and limit inferior. --- Linear equation. --- Maxima and minima. --- Maximal function. --- Metric space. --- Minimal surface. --- Multiple integral. --- Nonlinear system. --- Obstacle problem. --- Open set. --- Partial derivative. --- Quantity. --- Semi-continuity. --- Singular solution. --- Smoothness. --- Sobolev space. --- Special case. --- Stationary point. --- Subsequence. --- Subset. --- Theorem. --- Topological property. --- Topology. --- Uniform convergence. --- Variational inequality. --- Weak formulation. --- Weak solution.
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Based on seven lecture series given by leading experts at a summer school at Peking University, in Beijing, in 1984. this book surveys recent developments in the areas of harmonic analysis most closely related to the theory of singular integrals, real-variable methods, and applications to several complex variables and partial differential equations. The different lecture series are closely interrelated; each contains a substantial amount of background material, as well as new results not previously published. The contributors to the volume are R. R. Coifman and Yves Meyer, Robert Fcfferman,Carlos K. Kenig, Steven G. Krantz, Alexander Nagel, E. M. Stein, and Stephen Wainger.
Harmonic analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Analytic function. --- Asymptotic formula. --- Bergman metric. --- Bernhard Riemann. --- Bessel function. --- Biholomorphism. --- Boundary value problem. --- Bounded mean oscillation. --- Bounded operator. --- Boundedness. --- Cauchy's integral formula. --- Characteristic function (probability theory). --- Characterization (mathematics). --- Coefficient. --- Commutator. --- Complexification (Lie group). --- Continuous function. --- Convolution. --- Degeneracy (mathematics). --- Differential equation. --- Differential operator. --- Dirac delta function. --- Dirichlet problem. --- Equation. --- Estimation. --- Existence theorem. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Fatou's theorem. --- Fourier analysis. --- Fourier integral operator. --- Fourier transform. --- Fredholm theory. --- Fubini's theorem. --- Function (mathematics). --- Functional calculus. --- Fundamental solution. --- Gaussian curvature. --- Hardy space. --- Harmonic function. --- Harmonic measure. --- Heisenberg group. --- Hilbert space. --- Hilbert transform. --- Hodge theory. --- Holomorphic function. --- Hyperbolic partial differential equation. --- Hölder's inequality. --- Infimum and supremum. --- Integration by parts. --- Interpolation theorem. --- Intersection (set theory). --- Invertible matrix. --- Isometry group. --- Laplace operator. --- Laplace's equation. --- Lebesgue measure. --- Linear map. --- Lipschitz continuity. --- Lipschitz domain. --- Lp space. --- Mathematical induction. --- Mathematical physics. --- Maximal function. --- Maximum principle. --- Measure (mathematics). --- Newtonian potential. --- Non-Euclidean geometry. --- Number theory. --- Operator theory. --- Oscillatory integral. --- Parameter. --- Partial derivative. --- Partial differential equation. --- Polynomial. --- Power series. --- Product metric. --- Radon–Nikodym theorem. --- Riemannian manifold. --- Riesz representation theorem. --- Scientific notation. --- Several complex variables. --- Sign (mathematics). --- Simultaneous equations. --- Singular function. --- Singular integral. --- Sobolev space. --- Square (algebra). --- Statistical hypothesis testing. --- Stokes' theorem. --- Support (mathematics). --- Tangent space. --- Tensor product. --- Theorem. --- Trigonometric series. --- Uniformization theorem. --- Variable (mathematics). --- Vector field.
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Kiyosi Itô's greatest contribution to probability theory may be his introduction of stochastic differential equations to explain the Kolmogorov-Feller theory of Markov processes. Starting with the geometric ideas that guided him, this book gives an account of Itô's program. The modern theory of Markov processes was initiated by A. N. Kolmogorov. However, Kolmogorov's approach was too analytic to reveal the probabilistic foundations on which it rests. In particular, it hides the central role played by the simplest Markov processes: those with independent, identically distributed increments. To remedy this defect, Itô interpreted Kolmogorov's famous forward equation as an equation that describes the integral curve of a vector field on the space of probability measures. Thus, in order to show how Itô's thinking leads to his theory of stochastic integral equations, Stroock begins with an account of integral curves on the space of probability measures and then arrives at stochastic integral equations when he moves to a pathspace setting. In the first half of the book, everything is done in the context of general independent increment processes and without explicit use of Itô's stochastic integral calculus. In the second half, the author provides a systematic development of Itô's theory of stochastic integration: first for Brownian motion and then for continuous martingales. The final chapter presents Stratonovich's variation on Itô's theme and ends with an application to the characterization of the paths on which a diffusion is supported. The book should be accessible to readers who have mastered the essentials of modern probability theory and should provide such readers with a reasonably thorough introduction to continuous-time, stochastic processes.
Markov processes. --- Stochastic difference equations. --- Itō, Kiyosi, --- Analysis, Markov --- Chains, Markov --- Markoff processes --- Markov analysis --- Markov chains --- Markov models --- Models, Markov --- Processes, Markov --- Itō, K. --- Ito, Kiesi, --- Itō, Kiyoshi, --- 伊藤淸, --- 伊藤清, --- Itō, Kiyosi, --- Itō, Kiyosi, 1915-2008. --- Stochastic difference equations --- Difference equations --- Stochastic processes --- Abelian group. --- Addition. --- Analytic function. --- Approximation. --- Bernhard Riemann. --- Bounded variation. --- Brownian motion. --- Central limit theorem. --- Change of variables. --- Coefficient. --- Complete metric space. --- Compound Poisson process. --- Continuous function (set theory). --- Continuous function. --- Convergence of measures. --- Convex function. --- Coordinate system. --- Corollary. --- David Hilbert. --- Decomposition theorem. --- Degeneracy (mathematics). --- Derivative. --- Diffeomorphism. --- Differentiable function. --- Differentiable manifold. --- Differential equation. --- Differential geometry. --- Dimension. --- Directional derivative. --- Doob–Meyer decomposition theorem. --- Duality principle. --- Elliptic operator. --- Equation. --- Euclidean space. --- Existential quantification. --- Fourier transform. --- Function space. --- Functional analysis. --- Fundamental solution. --- Fundamental theorem of calculus. --- Homeomorphism. --- Hölder's inequality. --- Initial condition. --- Integral curve. --- Integral equation. --- Integration by parts. --- Invariant measure. --- Itô calculus. --- Itô's lemma. --- Joint probability distribution. --- Lebesgue measure. --- Linear interpolation. --- Lipschitz continuity. --- Local martingale. --- Logarithm. --- Markov chain. --- Markov process. --- Markov property. --- Martingale (probability theory). --- Normal distribution. --- Ordinary differential equation. --- Ornstein–Uhlenbeck process. --- Polynomial. --- Principal part. --- Probability measure. --- Probability space. --- Probability theory. --- Pseudo-differential operator. --- Radon–Nikodym theorem. --- Representation theorem. --- Riemann integral. --- Riemann sum. --- Riemann–Stieltjes integral. --- Scientific notation. --- Semimartingale. --- Sign (mathematics). --- Special case. --- Spectral sequence. --- Spectral theory. --- State space. --- State-space representation. --- Step function. --- Stochastic calculus. --- Stochastic. --- Stratonovich integral. --- Submanifold. --- Support (mathematics). --- Tangent space. --- Tangent vector. --- Taylor's theorem. --- Theorem. --- Theory. --- Topological space. --- Topology. --- Translational symmetry. --- Uniform convergence. --- Variable (mathematics). --- Vector field. --- Weak convergence (Hilbert space). --- Weak topology.
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This book has as its subject the boundary value theory of holomorphic functions in several complex variables, a topic that is just now coming to the forefront of mathematical analysis. For one variable, the topic is classical and rather well understood. In several variables, the necessary understanding of holomorphic functions via partial differential equations has a recent origin, and Professor Stein's book, which emphasizes the potential-theoretic aspects of the boundary value problem, should become the standard work in the field.Originally published in 1972.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Mathematical potential theory --- Holomorphic functions --- Harmonic functions --- Holomorphic functions. --- Harmonic functions. --- Fonctions de plusieurs variables complexes. --- Functions of several complex variables --- Functions, Harmonic --- Laplace's equations --- Bessel functions --- Differential equations, Partial --- Fourier series --- Harmonic analysis --- Lamé's functions --- Spherical harmonics --- Toroidal harmonics --- Functions, Holomorphic --- Absolute continuity. --- Absolute value. --- Addition. --- Ambient space. --- Analytic function. --- Arbitrarily large. --- Bergman metric. --- Borel measure. --- Boundary (topology). --- Boundary value problem. --- Bounded set (topological vector space). --- Boundedness. --- Brownian motion. --- Calculation. --- Change of variables. --- Characteristic function (probability theory). --- Combination. --- Compact space. --- Complex analysis. --- Complex conjugate. --- Computation. --- Conformal map. --- Constant term. --- Continuous function. --- Coordinate system. --- Corollary. --- Cramer's rule. --- Determinant. --- Diameter. --- Dimension. --- Elliptic operator. --- Estimation. --- Existential quantification. --- Explicit formulae (L-function). --- Exterior (topology). --- Fatou's theorem. --- Function space. --- Green's function. --- Green's theorem. --- Haar measure. --- Half-space (geometry). --- Harmonic function. --- Hilbert space. --- Holomorphic function. --- Hyperbolic space. --- Hypersurface. --- Hölder's inequality. --- Invariant measure. --- Invertible matrix. --- Jacobian matrix and determinant. --- Line segment. --- Linear map. --- Lipschitz continuity. --- Local coordinates. --- Logarithm. --- Majorization. --- Matrix (mathematics). --- Maximal function. --- Measure (mathematics). --- Minimum distance. --- Natural number. --- Normal (geometry). --- Open set. --- Order of magnitude. --- Orthogonal complement. --- Orthonormal basis. --- Parameter. --- Poisson kernel. --- Positive-definite matrix. --- Potential theory. --- Projection (linear algebra). --- Quadratic form. --- Quantity. --- Real structure. --- Requirement. --- Scientific notation. --- Sesquilinear form. --- Several complex variables. --- Sign (mathematics). --- Smoothness. --- Subgroup. --- Subharmonic function. --- Subsequence. --- Subset. --- Summation. --- Tangent space. --- Theorem. --- Theory. --- Total variation. --- Transitive relation. --- Transitivity. --- Transpose. --- Two-form. --- Unit sphere. --- Unitary matrix. --- Vector field. --- Vector space. --- Volume element. --- Weak topology.
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Inequalities appear in various fields of natural science and engineering. Classical inequalities are still being improved and/or generalized by many researchers. That is, inequalities have been actively studied by mathematicians. In this book, we selected the papers that were published as the Special Issue ‘’Inequalities’’ in the journal Mathematics (MDPI publisher). They were ordered by similar topics for readers’ convenience and to give new and interesting results in mathematical inequalities, such as the improvements in famous inequalities, the results of Frame theory, the coefficient inequalities of functions, and the kind of convex functions used for Hermite–Hadamard inequalities. The editor believes that the contents of this book will be useful to study the latest results for researchers of this field.
quantum estimates --- Montgomery identity --- power inequalities --- positive linear map --- Hilbert C*-module --- Hermite–Hadamard type inequality --- Steffensen’s inequality --- Hilbert space --- Hadamard fractional integrals --- K-dual --- adjointable operator --- analytic functions --- special means --- geometrically convex function --- h2)-convex --- proportional fractional derivative --- commutator --- quasi-convex --- Katugampola fractional integrals --- Euler-Maclaurin summation formula --- starlike functions --- strongly ?-convex functions --- g-frame --- interval-valued functions --- twice differentiable convex functions --- Taylor theorem --- exponential inequalities --- g-Bessel sequence --- Riemann–Liouville and Caputo proportional fractional initial value problem --- frame --- Fejér’s inequality --- weight function --- Hermite-Hadamard type inequalities --- Gronwall–Bellman inequality --- ?-variation --- Hölder’s inequality --- majorization inequality --- alternate dual frame --- half-discrete Hardy-Hilbert’s inequality --- parameter --- Power mean inequality --- Riemann–Liouville fractional integrals --- reverse inequality --- weaving frame operator --- Fink’s identity --- pseudo-inverse --- operator inequality --- Hermite-Hadamard inequality --- one-sided weighted Morrey space --- Green functions --- weaving K-frame --- operator Kantorovich inequality --- higher order convexity --- weaving frame --- (h1 --- one-sided weighted Campanato space --- Fekete-Szegö inequality --- convex functions --- refined inequality --- trigonometric inequalities --- one-sided singular integral
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