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Functional analysis. --- Hilbert algebras. --- Operator theory.

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A signi?cant sector of the development of spectral theory outside the classical area of Hilbert space may be found amongst at multipliers de?ned on a complex commutative Banach algebra A. Although the general theory of multipliers for abstract Banach algebras has been widely investigated by several authors, it is surprising how rarely various aspects of the spectral theory, for instance Fredholm theory and Riesz theory, of these important classes of operators have been studied. This scarce consideration is even more surprising when one observes that the various aspects of spectral t- ory mentioned above are quite similar to those of a normal operator de?ned on a complex Hilbert space. In the last ten years the knowledge of the spectral properties of multip- ers of Banach algebras has increased considerably, thanks to the researches undertaken by many people working in local spectral theory and Fredholm theory. This research activity recently culminated with the publication of the book of Laursen and Neumann [214], which collects almost every thing that is known about the spectral theory of multipliers.

Fredholm equations. --- Spectral theory (Mathematics) --- Banach algebras. --- Operator theory. --- Functional analysis. --- Harmonic analysis. --- Operator Theory. --- Functional Analysis. --- Abstract Harmonic Analysis. --- Analysis (Mathematics) --- Functions, Potential --- Potential functions --- Banach algebras --- Calculus --- Mathematical analysis --- Mathematics --- Bessel functions --- Fourier series --- Harmonic functions --- Time-series analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Functional analysis --- Equations, Fredholm

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In contrast to other books devoted to the averaging method and the method of integral manifolds, in the present book we study oscillation systems with many varying frequencies. In the process of evolution, systems of this type can pass from one resonance state into another. This fact considerably complicates the investigation of nonlinear oscillations. In the present monograph, a new approach based on exact uniform estimates of oscillation integrals is proposed. On the basis of this approach, numerous completely new results on the justification of the averaging method and its applications are obtained and the integral manifolds of resonance oscillation systems are studied. This book is intended for a wide circle of research workers, experts, and engineers interested in oscillation processes, as well as for students and post-graduate students specialized in ordinary differential equations.

Nonlinear oscillations. --- Differential Equations. --- Differential equations, partial. --- Fourier analysis. --- Functional analysis. --- Mathematics. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Fourier Analysis. --- Functional Analysis. --- Applications of Mathematics. --- Differential equations. --- Partial differential equations. --- Applied mathematics. --- Engineering mathematics. --- Engineering --- Engineering analysis --- Mathematical analysis --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis, Fourier --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Mathematics --- Nonlinear theories --- Oscillations

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Topological spaces. --- Topology. --- Mathematics. --- Mathematical optimization. --- Distribution (Probability theory. --- Functional analysis. --- Measure and Integration. --- Calculus of Variations and Optimal Control; Optimization. --- Probability Theory and Stochastic Processes. --- Functional Analysis. --- Measure theory. --- Calculus of variations. --- Probabilities. --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)

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The book is devoted to various constructions of sets which are nonmeasurable with respect to invariant (more generally, quasi-invariant) measures. Our starting point is the classical Vitali theorem stating the existence of subsets of the real line which are not measurable in the Lebesgue sense. This theorem stimulated the development of the following interesting topics in mathematics:1. Paradoxical decompositions of sets in finite-dimensional Euclidean spaces;2. The theory of non-real-valued-measurable cardinals;3. The theory of invariant (quasi-invariant)extensions of invarian

Measure theory. --- Functional analysis. --- Set theory. --- Aggregates --- Classes (Mathematics) --- Ensembles (Mathematics) --- Mathematical sets --- Sets (Mathematics) --- Theory of sets --- Logic, Symbolic and mathematical --- Mathematics --- Functional calculus --- Calculus of variations --- Functional equations --- Integral equations --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra)