Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Inequalities (Mathematics) --- Integral transforms. --- Transform calculus --- Integral equations --- Transformations (Mathematics) --- Processes, Infinite --- Analytical spaces --- Differential equations

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This informal introduction provides a fresh perspective on isomorphism theory, which is the branch of ergodic theory that explores the conditions under which two measure preserving systems are essentially equivalent. It contains a primer in basic measure theory, proofs of fundamental ergodic theorems, and material on entropy, martingales, Bernoulli processes, and various varieties of mixing. Original proofs of classic theorems - including the Shannon-McMillan-Breiman theorem, the Krieger finite generator theorem, and the Ornstein isomorphism theorem - are presented by degrees, together with helpful hints that encourage the reader to develop the proofs on their own. Hundreds of exercises and open problems are also included, making this an ideal text for graduate courses. Professionals needing a quick review, or seeking a different perspective on the subject, will also value this book.

Ergodic theory. --- Isomorphisms (Mathematics) --- Categories (Mathematics) --- Group theory --- Morphisms (Mathematics) --- Set theory --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics)

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

For more than 200 years, the Fourier Transform has been one of the most important mathematical tools for understanding the dynamics of linear wave trains. Nonlinear Ocean Waves and the Inverse Scattering Transform presents the development of the nonlinear Fourier analysis of measured space and time series, which can be found in a wide variety of physical settings including surface water waves, internal waves, and equatorial Rossby waves. This revolutionary development will allow hyperfast numerical modelling of nonlinear waves, greatly advancing our understanding of oceanic surface a

Ocean waves. --- Nonlinear waves. --- Inverse scattering transform. --- Nonlinear wave equations. --- Wave equation --- Scattering transform, Inverse --- Transform, Inverse scattering --- Scattering (Mathematics) --- Transformations (Mathematics) --- Nonlinear theories --- Wave-motion, Theory of --- Waves --- Breakers --- Sea waves --- Surf --- Swell --- Oceanography --- Water waves

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This textbook presents an elementary introduction to generalized functions by using Sato's approach of hyperfunctions which is based on complex function theory. This very intuitive and appealing approach has particularly great computational power.   The concept of hyperfunctions and their analytic properties is introduced and discussed in detail in the first two chapters of the book. Thereafter the focus lies on generalizing the (classical) Laplace, Fourier, Hilbert, Mellin, and Hankel transformations to hyperfunctions. Applications to integral and differential equations and a rich variety of concrete examples accompany the text throughout the book.   Requiring only standard knowledge of the theory of complex variables, the material is easily accessible for advanced undergraduate or graduate students. It serves as well as a reference for researchers in pure and applied mathematics, engineering and physics.  .

Electronic books. -- local. --- Hyperfunctions. --- Integral transforms. --- Transformations (Mathematics). --- Mathematics --- Civil & Environmental Engineering --- Physical Sciences & Mathematics --- Engineering & Applied Sciences --- Operations Research --- Calculus --- Transformations (Mathematics) --- Transform calculus --- Mathematics. --- Fourier analysis. --- Operational calculus. --- Special functions. --- Computer mathematics. --- Integral Transforms, Operational Calculus. --- Special Functions. --- Computational Science and Engineering. --- Fourier Analysis. --- Integral equations --- Theory of distributions (Functional analysis) --- Algorithms --- Differential invariants --- Geometry, Differential --- Integral Transforms. --- Functions, special. --- Computer science. --- Analysis, Fourier --- Mathematical analysis --- Informatics --- Science --- Special functions --- Computer mathematics --- Electronic data processing --- Operational calculus --- Differential equations --- Electric circuits --- Mathematical analysis. --- Integral Transforms and Operational Calculus. --- Data processing. --- 517.1 Mathematical analysis

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

The theory of operator semigroups was essentially discovered in the early 1930s. Since then, the theory has developed into a rich and exciting area of functional analysis and has been applied to various mathematical topics such as Markov processes, the abstract Cauchy problem, evolution equations, and mathematical physics. This self-contained monograph focuses primarily on the theoretical connection between the theory of operator semigroups and spectral theory. Divided into three parts with a total of twelve distinct chapters, this book gives an in-depth account of the subject with numerous examples, detailed proofs, and a brief look at a few applications. Topics include: * The Hille–Yosida and Lumer–Phillips characterizations of semigroup generators * The Trotter–Kato approximation theorem * Kato’s unified treatment of the exponential formula and the Trotter product formula * The Hille–Phillips perturbation theorem, and Stone’s representation of unitary semigroups * Generalizations of spectral theory’s connection to operator semigroups * A natural generalization of Stone’s spectral integral representation to a Banach space setting With a collection of miscellaneous exercises at the end of the book and an introductory chapter examining the basic theory involved, this monograph is suitable for second-year graduate students interested in operator semigroups.

Semigroups of operators. --- Spectral theory (Mathematics). --- Semigroups of operators --- Spectral theory (Mathematics) --- Calculus --- Mathematics --- Physical Sciences & Mathematics --- Operators, Semigroups of --- Mathematics. --- Algebra. --- Group theory. --- Operator theory. --- Operator Theory. --- Group Theory and Generalizations. --- Functional analysis --- Hilbert space --- Measure theory --- Transformations (Mathematics) --- Operator theory --- Groups, Theory of --- Substitutions (Mathematics) --- Algebra --- Mathematical analysis