Kategoria BISAC: Mathematics >> Functional Analysis

This book presents an exposition of spherical functions on compact symmetric spaces, from the viewpoint of Cartan-Selberg. Representation theory, invariant differential operators, and invariant integral operators play an important role in the exposition. The author treats compact symmetric pairs, spherical representations for compact symmetric pairs, the fundamental groups of compact symmetric spaces, and the radial part of an invariant differential operator. Also explored are the classical results for spheres and complex projective spaces and the relation between spherical functions and...

Treats free probability theory, which has been extensively developed since the early 1980s. This work focuses on entropy and the random matrix model approach. It is suitable as a reference for mathematicians interested in free probability theory and can se

Kuranishi proved that any abstract strongly pseudo convex CR-structure of real dimension $geq 9$ can be locally embedded in a complex euclidean space. For the case of real dimension $=3$, there is the famous Nirenberg counter example, but the cases of real dimension $=5$ or 7 were left open. This book presents the result for real dimension $=7$.

The mathematics of the quantum theory of fields has been a continuing puzzle to mathematicians and physicists for many decades. Based on the author's 1960 lectures in Boulder, this title looks at some of the unresolved mathematical questions in the quantum field theory of the time, with an emphasis on problems coming from perturbation theory.

An abstract Volterra operator is, roughly speaking, a compact operator in a Hilbert space whose spectrum consists of a single point $lambda=0$. This book, intended for mathematicians interested in functional analysis and its applications, discusses the mai

All needed notions are developed within the book: with the exception of fundamentals which are presented in introductory lectures, no other knowledge is assumed

Provides a more in-depth introduction to the subject than other existing books in this area

Over 400 exercises including hints for solutions are included

Delta Functions has now been updated, restructured and modernised into a second edition, to answer specific difficulties typically found by students encountering delta functions for the first time. In particular, the treatment of the Laplace transform has been revised with this in mind. The chapter on Schwartz distributions has been considerably extended and the book is supplemented by a fuller review of Nonstandard Analysis and a survey of alternative infinitesimal treatments of generalised functions.

Dealing with a difficult subject in a simple and straightforward way, the text is...

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. There has been much progress in a number of problems concerning local - pects of spectral analysis and spectral synthesis on homogeneous spaces. The study oftheseproblemsturnsouttobecloselyrelatedtoavarietyofquestionsinharmonic analysis, complex analysis, partial differential equations, integral geometry, appr- imation theory, and other branches of contemporary mathematics. The present book describes recent advances in this...

This text is an introduction to functional analysis which requires readers to have a minimal background in linear algebra and real analysis at the first-year graduate level. Prerequisite knowledge of general topology or Lebesgue integration is not required. The book explains the principles and applications of functional analysis and explores the development of the basic properties of normed linear, inner product spaces and continuous linear operators defined in these spaces. Though Lebesgue integral is not discussed, the book offers an in-depth knowledge on the numerous applications of the...

Nonnegative matrices and positive operators are widely applied in science, engineering, and technology. This book provides the basic theory and several typical modern science and engineering applications of nonnegative matrices and positive operators, including the fundamental theory, methods, numerical analysis, and applications in the Google search engine, computational molecular dynamics, and wireless communications.Unique features of this book include the combination of the theories of nonnegative matrices and positive operators as well as the emphasis on applications of nonnegative...

Presents Real & Complex Analysis Together Using a Unified Approach
A two-semester course in analysis at the advanced undergraduate or first-year graduate level

Unlike other undergraduate-level texts, Real and Complex Analysis develops both the real and complex theory together. It takes a unified, elegant approach to the theory that is consistent with the recommendations of the MAA s 2004 Curriculum Guide.

By presenting real and complex analysis together, the authors illustrate the connections and differences between these two branches of...

The core of this book are Banach spaces of analytic functions on the unit disk. Not only do we study how operators like composition operators, multiplication operators and weighted composition operators behave when operating on different such spaces, but also how the Banach spaces in question relate to other Banach spaces. We study the dual and predual spaces of Banach spaces and introduce some new spaces in the process. Properties of the operators mentioned above that we investigate are amongst others; the spectrum, the closed range property and boundedness. The book is based on three...

This is a book on holomorphic operator functions of a single variable and their - plications, whichisfocussedontherelationsbetweenlocalandglobaltheories.Itis based on methods and technics of Complex analysis of scalar and matrix functions of several variables. The applications concern: interpolation, holomorphic families of subspaces and frames, spectral theory of polynomials with operator coe?cients, holomorphic equivalence and diagonalization, and Plemelj-Muschelishvili fact- ization. The book also contains a theory of Wiener-Hopf integral equations with operator-valued kernels and a theory...

Piezoelectricity has been a steadily growing field, with recent advances made by researchers from applied physics, acoustics, materials science, and engineering. This collective work presents a comprehensive treatment of selected advanced topics in the subject. The book is written for an intermediate graduate level and is intended for researchers, mechanical engineers, and applied mathematicians interested in the advances and new applications in piezoelectricity.

In the past decade, the mathematics of superconductivity has been the subject of intense study. This book examines in detail the nonlinear Ginzburg-Landau (GL) functional, the model most commonly used. Specifically, cases in the presence of a strong magnetic field and with a sufficiently large GL parameter kappa are covered.

Key topics and features:

*Provides a concrete introduction to techniques in spectral theory and PDEs

*Offers a complete analysis of the two-dimensional GL-functional with large kappa in the presence of a magnetic field

...

With many new concrete examples and historical notes, Topological Vector Spaces, Second Edition provides one of the most thorough and up-to-date treatments of the Hahn-Banach theorem. This edition explores the theorem's connection with the axiom of choice, discusses the uniqueness of Hahn-Banach extensions, and includes an entirely new chapter on vector-valued Hahn-Banach theorems. It also considers different approaches to the Banach-Stone theorem as well as variations of the theorem.

The book covers locally convex spaces; barreled, bornological, and webbed...

The study of critical points has grown rapidly in recent years, finding applications in most every science. This book spans the material required for those who want a survey of modern critical point theory.

Key features:

*Provides an introduction to linking methods and generalizations

*Explains the fundamentals of minimax systems

*Many examples and applications

This text starts at the foundations of the field, and is accessible with some background in functional analysis. As such, the book is ideal for classroom of...

Let A be the W*-algebra, L1(E(0), u), where E(0) is a fnite set and u is a probability measure with full support. Let P: A->A be a completely positive unital map. In the present context, P is given by a stochastic matrix. We study the properties of P that are refected in the dilation theory developed by Muhly and Solel in Int. J. Math. 13, 2002. Let H be the Hilbert space L2(E(0), u) and let pi: A -> B(H) the representation of A given by multiplication. Form the Stinespring space H1. Then X is a W*-correspondence over P is expressed through a completely contractive representation T of X on H....

The groups Sp(1;R), O(3;4) form a dual pair in the sense of Howe. This leads to a correspondence of irreducible unitary representations between the double connected cover of Sp(1;R) and some irreducible unitary representations of O(3;4). By a property of double transitivity, Rallis & Schiffmann showed that the restriction of the resulting representation to G2 remains irreducible, but don't compute the characters of these representations. Neither do they compute the lowest term of the expansion of such a character, which should be the Fourier transform of an orbital integral corresponding to a...

The Kirillov character formula gives a striking correspondence between the unitary irreducible representations of a compact semisimple Lie group and its set of integral orbits on the dual of its Lie algebra. In this thesis, the same correspondence is derived without the use of character theory. It is shown to be related to the convexity properties of the support of the Weyl functional calculus of the infinitesimal generators of the representation. This result uses Edward Nelson's theory of "operants" in a fundamental way. This had been developed to put Feynman's operator calculus on a...