Functional analysis and transforms

Feynman path integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non-relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology.

Interpolation of functions is one of the basic part of Approximation Theory.

Pseudo-differential operators were initiated by Kohn, Nirenberg and Hormander in the sixties of the last century.

In this monograph on twistor theory and its applications to harmonic map theory, a central theme is the interplay between the complex homogeneous geometry of flag manifolds and the real homogeneous geometry of symmetric spaces.

The Pontryagin-van Kampen duality theorem and the Bochner theorem on positive-definite functions are known to be true for certain abelian topological groups that are not locally compact.

Wavelets are a recently developed tool for the analysis and synthesis of functions; their simplicity, versatility and precision makes them valuable in many branches of applied mathematics.

Feynman path integrals integrals, suggested heuristically by Feynman in the 40s, have become the basis of much of contemporary physics, from non relativistic quantum mechanics to quantum fields, including gauge fields, gravitation, cosmology.

The Dirichlet problem has a very long history in mathematics and its importance in partial differential equations, harmonic analysis, potential theory and the applied sciences is well-known.

Since the late 1980s, Toeplitz operators and matrices have remained a ?

Nonlinear analysis has developed rapidly in the last three decades.

The theory of mean periodic functions is a subject which goes back to works of Littlewood, Delsarte, John and that has undergone a vigorous development in recent years.

The contents of this monograph fall within the general area of nonlinear functional analysis and applications.

Since the first edition of this book was published several new developments have been made in the field of the moire theory.

This book provides an introduction to the ideas and methods of linear fu- tional analysis at a level appropriate to the ?

A rigorous but accessible treatment of the subject intertwining theoretical techniques with hands-on laboratory instruction and divided into three parts, this book covers various aspects of the digital signal processing (DSP) "e;problem"e;.

The abstract concepts of metric spaces are often perceived as difficult.

Aimed at graduate and postgraduate students and researchers in mathematics and the applied sciences, this book provides an introductory account of scattering phenomena and a guide to the technical requirements for investigating wave scattering problems.

Developed from a course taught to senior undergraduates, this book provides a unified introduction to Fourier analysis and special functions based on the Sturm-Liouville theory in L2.

Since the last century, the postulational method and an abstract point of view have played a vital role in the development of modern mathematics.

Variational and boundary integral equation techniques are two of the most useful methods for solving time-dependent problems described by systems of equations of the form 2 ?

Safety critical and high-integrity systems, such as industrial plants and economic systems can be subject to abrupt changes - for instance due to component or interconnection failure, and sudden environment changes etc.

Perturbations of Positive Semigroups with Applications is a self-contained introduction to semigroup theory with emphasis on positive semigroups on Banach lattices and perturbation techniques.

This book serves as a textbook for an analytical mechanics course, a fundamental subject of physics, that pays special attention to important topics that are not discussed in most standard textbooks.

This monograph presents the existence and properties of both weak and strong solutions to the problems of the flow of a compressible fluid in a domain whose motion is prescribed.

Inverse problems lie at the core of scientific discovery, enabling us to determine causes from observed consequences.

This textbook offers a self-contained introduction to probability, covering all topics required for further study in stochastic processes and stochastic analysis, as well as some advanced topics at the interface between probability and functional analysis.

Spectral properties for Schrodinger operators are a major concern in quantum mechanics both in physics and in mathematics.

This book is devoted to real analysis methods for the problem of constructing Markov processes with boundary conditions in probability theory.

This book introduces readers to order analysis and various aspects of deep learning, and describes important connections to optimization, such as nonlinear optimization as well as vector and set optimization.

This comprehensive book offers an accessible introduction to Fourier analysis and distribution theory, blending classical mathematical theory with a wide range of practical applications.

This monograph presents a study of newly developed guaranteed computational methodologies for eigenvalue problems of self-adjoint differential operators.

Data-Driven, Nonparametric, Adaptive Control Theory introduces a novel approach to the control of deterministic, nonlinear ordinary differential equations affected by uncertainties.

Data-Driven, Nonparametric, Adaptive Control Theory introduces a novel approach to the control of deterministic, nonlinear ordinary differential equations affected by uncertainties.

This book offers a comprehensive introduction by three of the leading experts in the field, collecting fundamental results and open problems in a single volume.

This monograph is about monotone complete C*-algebras, their properties and the new classification theory.

The discrete Fourier transform (DFT) is an extremely useful tool that finds application in many different disciplines.

Real Analysis: Measures, Integrals and Applications is devoted to the basics of integration theory and its related topics.

In this book, there is a strong emphasis on application with the necessary mathematical grounding.