Functional analysis and transforms

This monograph is an account of some problems involving diffusion or diffusion with simultaneous reaction that can be illuminated by the use of variational principles.

Recent research has produced a large number of results concerning the Stone-Cech compactification or involving it in a central manner.

Die vorliegende Darstellung der klassischen Funktionentheorie ist aus Nachschriften, die wir seit geraumer Zeit von unseren Vorlesungen anfertigen ließen, entstanden.

Generalizations of the classical concept of a convexfunction have been proposed in various fields such aseconomics, management science, engineering, statistics andapplied sciences during the second half of this century.

The present work is an extended version of a manuscript of a course which the author taught at the University of Hamburg during summer 1969.

The aim of this book is to give a systematic study of questions con- cerning existence, uniqueness and regularity of solutions of linear partial differential equations and boundary problems.

In recent years important progress has been made in the study of semi-groups of operators from the viewpoint of approximation theory.

This volume, setting out the theory of positive maps as it stands today, reflects the rapid growth in this area of mathematics since it was recognized in the 1990s that these applications of C*-algebras are crucial to the study of entanglement in quantum theory.

The theory of slice regular functions over quaternions is the central subject of the present volume.

Many phenomena in engineering and mathematical physics can be modeled by means of boundary value problems for a certain elliptic differential operator in a given domain.

This volume mainly deals with the dynamics of finitely valued sequences, and more specifically, of sequences generated by substitutions and automata.

The present book is about the Askey scheme and the q-Askey scheme, which are graphically displayed right before chapter 9 and chapter 14, respectively.

One of the beautiful results in the representation theory of the finite groups is McKay's theorem on a correspondence between representations of the binary polyhedral group of SU(2) and vertices of an extended simply-laced Dynkin diagram.

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 ?

This book presents a rigorous mathematical treatment of the theory of pricing and hedging of derivative securities by the principle of "e;no arbitrage"e;.

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.