Functional analysis and transforms

Algebras of bounded operators are familiar, either as C*-algebras or as von Neumann algebras.

Infinitesimal analysis, once a synonym for calculus, is now viewed as a technique for studying the properties of an arbitrary mathematical object by discriminating between its standard and nonstandard constituents.

Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations.

This monograph is intended to be a complete treatment of the metrical the- ory of the (regular) continued fraction expansion and related representations of real numbers.

The monograph presents some of the authors' recent and original results concerning boundedness and compactness problems in Banach function spaces both for classical operators and integral transforms defined, generally speaking, on nonhomogeneous spaces.

Two-and three-level difference schemes for discretisation in time, in conjunction with finite difference or finite element approximations with respect to the space variables, are often used to solve numerically non- stationary problems of mathematical physics.

Over the past few years a certain shift of focus within the theory of algebras of generalized functions (in the sense of J.

The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point.

Despite their novelty, wavelets have a tremendous impact on a number of modern scientific disciplines, particularly on signal and image analysis.

Historically, complex analysis and geometrical function theory have been inten- sively developed from the beginning of the twentieth century.

This monograph on quantum wires and quantum devices is a companion vol- ume to the author's Quantum Chaos and Mesoscopic Systems (Kluwer, Dordrecht, 1997).

It seems hard to believe, but mathematicians were not interested in integration problems on infinite-dimensional nonlinear structures up to 70s of our century.

In [Hardy and Williams, 1986] the authors exploited a very simple idea to obtain a linear congruence involving class numbers of imaginary quadratic fields modulo a certain power of 2.

Preface to the English Edition The present monograph is a revised and enlarged alternative of the author's monograph [19] which was devoted to the development of a unified approach to studying differential inclusions, whose values of the right hand sides are compact, not necessarily convex subsets of a Banach space.

Iteration regularization, i.

To summarize briefly, this book is devoted to an exposition of the foundations of pseudo differential equations theory in non-smooth domains.

The notion of a dominated or rnajorized operator rests on a simple idea that goes as far back as the Cauchy method of majorants.

This book is an attempt to give a systematic presentation of results and meth- ods which concern the fixed point theory of multivalued mappings and some of its applications.

The present volume contains the proceedings of the workshop on "e;Minimax Theory and Applications"e; that was held during the week 30 September - 6 October 1996 at the "e;G.

This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic.

This volume considers various methods for constructing cubature and quadrature formulas of arbitrary degree.

The aim of this volume is to make available to a large audience recent material in nonlinear functional analysis that has not been covered in book format before.

This book is intended as a continuation of my book "e;Parametrix Method in the Theory of Differential Complexes"e; (see [291]).

to the English Translation This is a concise guide to basic sections of modern functional analysis.

Mathematical modeling plays an essential role in science and engineering.

This book is an outgrowth of ideas originating from 1.

The theory of operator algebras acting on a Hilbert space was initiated in thirties by papers of Murray and von Neumann.

Approximation Theory, Wavelets and Applications draws together the latest developments in the subject, provides directions for future research, and paves the way for collaborative research.

Algebraic K-theory is a modern branch of algebra which has many important applications in fundamental areas of mathematics connected with algebra, topology, algebraic geometry, functional analysis and algebraic number theory.

Considering integral transformations of Volterra type, F.

The analytical basis of Navier-Stokes Equations in Irregular Domains is formed by coercive estimates, which enable proofs to be given of the solvability of the boundary value problems for Stokes and Navier-Stokes equations in weighted Sobolev and Holder spaces, and the investigation of the smoothness of their solutions.

Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known.

It is well known that the normal distribution is the most pleasant, one can even say, an exemplary object in the probability theory.

This volume contains several surveys focused on the ideas of approximate solutions, well-posedness and stability of problems in scalar and vector optimization, game theory and calculus of variations.

The intention of this book is to explain to a mathematician having no previous knowledge in this domain, what "e;noncommutative probability"e; is.

Numbers .

This monograph provides an introduction to the theory of topologies defined on the closed subsets of a metric space, and on the closed convex subsets of a normed linear space as well.

The main purpose of this handbook is to summarize and to put in order the ideas, methods, results and literature on the theory of random evolutions and their applications to the evolutionary stochastic systems in random media, and also to present some new trends in the theory of random evolutions and their applications.

The book Partial Differential Equations through Examples and Exercises has evolved from the lectures and exercises that the authors have given for more than fifteen years, mostly for mathematics, computer science, physics and chemistry students.

As our title suggests, there are two aspects in the subject of this book.

1 More than thirty years after its discovery by Abraham Robinson , the ideas and techniques of Nonstandard Analysis (NSA) are being applied across the whole mathematical spectrum,as well as constituting an im- portant field of research in their own right.

During the last few years, the theory of operator algebras, particularly non-self-adjoint operator algebras, has evolved dramatically, experiencing both international growth and interfacing with other important areas.

The present monograph consists of two parts.