Functional analysis and transforms

The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis.

The subject of this monograph is the quaternionic spectral theory based on the notion of S-spectrum.

This book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications.

This book offers a thorough guide starting from fundamental functional analysis leading to the coupling of Stokes and Darcy equations, including numerical analysis and scientific computing.

The main purpose of the book is to give a rigorous introduction to the most important and useful solution methods of various types of stochastic control problems for jump diffusions and their applications.

This is a book comprising selected papers of colleagues and friends of Heinrich Begehr on the occasion of his 80th birthday.

This book contains a multitude of challenging problems and solutions that are not commonly found in classical textbooks.

This monograph concerns the relationship between the local spectral theory and Fredholm theory of bounded linear operators acting on Banach spaces.

Based on the authors' research experience, this two-volume reference textbook focuses on the theory of generalized locally Toeplitz sequences and its applications.

This book deals with elliptic differential equations, providing the analytic background necessary for the treatment of associated spectral questions, and covering important topics previously scattered throughout the literature.

This book offers a user friendly, hands-on, and systematic introduction to applied and computational harmonic analysis: to Fourier analysis, signal processing and wavelets; and to their interplay and applications.

This book presents contributions from two workshops in algebraic and analytic microlocal analysis that took place in 2012 and 2013 at Northwestern University.

This book develops a spectral theory for the integrable system of 2-dimensional, simply periodic, complex-valued solutions u of the sinh-Gordon equation.

This book collects papers based on the XXXVI Bialowieza Workshop on Geometric Methods in Physics, 2017.

This book includes the texts of the survey lectures given by plenary speakers at the 11th International ISAAC Congress held in Vaxjo, Sweden, on 14-18 August, 2017.

Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations.

This book, which is a continuation of Almost Automorphic Type and Almost Periodic Type Functions in Abstract Spaces, presents recent trends and developments upon fractional, first, and second order semilinear difference and differential equations, including degenerate ones.

This monograph develops an operator viewpoint for functional equations in classical function spaces of analysis, thus filling a void in the mathematical literature.

Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations.

New technological innovations and advances in research in areas such as spectroscopy, computer tomography, signal processing, and data analysis require a deep understanding of function approximation using Fourier methods.

Concentration compactness is an important method in mathematical analysis which has been widely used in mathematical research for two decades.

This book presents a wide panorama of methods to investigate the spectral properties of block operator matrices.

After recalling essentials of analysis - including functional analysis, convexity, distribution theory and interpolation theory - this book handles two topics in detail: Fourier analysis, with emphasis on positivity and also on some function spaces and multiplier theorems; and one-parameter operator semigroups with emphasis on Feller semigroups and Lp-sub-Markovian semigroups.

In this volume two topics are discussed: the construction of Feller and Lp-sub-Markovian semigroups by starting with a pseudo-differential operator, and the potential theory of these semigroups and their generators.

Nonlinear semigroup theory is not only of intrinsic interest, but is also important in the study of evolution problems.

This book presents contemporary mathematical concepts and techniques including theories of summability, fixed point and non-absolute integration and applications, providing an overview of recent developments in the foundations of the field as well as its applications.

Separate and Joint Continuity presents and summarises the main ideas and theorems that have been developed on this topic, which lies at the interface between General Topology and Functional Analysis (and the geometry of Banach spaces in particular).

The authors explain the Fourier transform and its technical applications, especially in signal and system theory.

Stable solutions are ubiquitous in differential equations.

This book includes plenty of theorems which are considered to be useful supplement to all standard course-materials.

In its second installment, Innovative Integrals and Their Applications II explores multidimensional integral identities, unveiling powerful techniques for attacking otherwise intractable integrals, thus demanding ingenuity and novel approaches.

This text covers a first course in bilinear maps and tensor products intending to bring the reader from the beginning of functional analysis to the frontiers of exploration with tensor products.

In the first edition of his seminal introduction to wavelets, James S.

Providing a basic tool for studying nonlinear problems, Spectral Theory for Random and Nonautonomous Parabolic Equations and Applications focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems.

Until now, no book has systematically presented the recently developed concept of envelopes in function spaces.

Providing a unified account of nonrelativistic quantum mechanics, Fundamentals of Quantum Mechanics covers the principles and formalism of quantum mechanics and the development and application of general techniques for the solution of quantum mechanical problems.

Asymptotic Behavior: An Overview is designed to provide the reader with an exposition of some aspects of the oscillation theory of first order delay partial dynamic equations on time scales.

Several scientists learn only a first course in complex analysis, and hence they are not familiar with several important properties: every polygenic function defines a congruence of clocks; the basic properties of algebraic functions and abelian integrals; how mankind arrived at a rigorous definition of Riemann surfaces; the concepts of dianalytic structures and Klein surfaces; the Weierstrass elliptic functions; the automorphic functions discovered by Poincare' and their links with the theory of Fuchsian groups; the geometric structure of fractional linear transformations; Kleinian groups; the Heisenberg group and geometry of the complex ball; complex powers of elliptic operators and the theory of spectral zeta-functions; an assessment of the Poincare' and Dieudonne' definitions of the concept of asymptotic expansion.

Non-Newtonian Sequence Spaces with Applications presents an alternative to the usual calculus based on multiplication instead of addition.

This book deals with the determinants of linear operators in Euclidean, Hilbert and Banach spaces.

This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering.

This book helps students explore Fourier analysis and its related topics, helping them appreciate why it pervades many fields of mathematics, science, and engineering.

Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level.

Principles of Analysis: Measure, Integration, Functional Analysis, and Applications prepares readers for advanced courses in analysis, probability, harmonic analysis, and applied mathematics at the doctoral level.

Analytic Methods for Coagulation-Fragmentation Models is a two-volume set that provides a comprehensive exposition of the mathematical analysis of coagulation-fragmentation models.

Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods.

Written as a textbook, A First Course in Functional Analysis is an introduction to basic functional analysis and operator theory, with an emphasis on Hilbert space methods.

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject.

Applied Functional Analysis, Third Edition provides a solid mathematical foundation for the subject.

This book presents a unified algebraic approach to stabilization problems of linear boundary control systems with no assumption on finite-dimensional approximations to the original systems, such as the existence of the associated Riesz basis.