Bounded Integral Operators On L 2 Spaces

Author : P. R. Halmos,V. S. Sunder
Publisher : Springer Science & Business Media
Page : 147 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642670169

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Bounded Integral Operators on L 2 Spaces by P. R. Halmos,V. S. Sunder Pdf

The subject. The phrase "integral operator" (like some other mathematically informal phrases, such as "effective procedure" and "geometric construction") is sometimes defined and sometimes not. When it is defined, the definition is likely to vary from author to author. While the definition almost always involves an integral, most of its other features can vary quite considerably. Superimposed limiting operations may enter (such as L2 limits in the theory of Fourier transforms and principal values in the theory of singular integrals), IJ' spaces and abstract Banach spaces may intervene, a scalar may be added (as in the theory of the so-called integral operators of the second kind), or, more generally, a multiplication operator may be added (as in the theory of the so-called integral operators of the third kind). The definition used in this book is the most special of all. According to it an integral operator is the natural "continuous" generali zation of the operators induced by matrices, and the only integrals that appear are the familiar Lebesgue-Stieltjes integrals on classical non-pathological mea sure spaces. The category. Some of the flavor of the theory can be perceived in finite dimensional linear algebra. Matrices are sometimes considered to be an un natural and notationally inelegant way of looking at linear transformations. From the point of view of this book that judgement misses something.

Author : Paul Richard Halmos,V. S. Sunder
Publisher : Springer
Page : 160 pages
File Size : 47,6 Mb
Release : 1978
Category : Mathematics
ISBN : UOM:39015017294680

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Bounded Integral Operators on L2 Spaces by Paul Richard Halmos,V. S. Sunder Pdf

Author : George Olatokunbo Okikiolu
Publisher : Unknown
Page : 542 pages
File Size : 52,7 Mb
Release : 1971
Category : Mathematics
ISBN : UOM:39015015689493

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Aspects of the Theory of Bounded Integral Operators in Lp-spaces by George Olatokunbo Okikiolu Pdf

Author : David E. Edmunds,V.M Kokilashvili,Alexander Meskhi
Publisher : Springer Science & Business Media
Page : 655 pages
File Size : 48,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401599221

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Bounded and Compact Integral Operators by David E. Edmunds,V.M Kokilashvili,Alexander Meskhi Pdf

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. Itfocuses onintegral operators naturally arising in boundary value problems for PDE, the spectral theory of differential operators, continuum and quantum mechanics, stochastic processes etc. The book may be considered as a systematic and detailed analysis of a large class of specific integral operators from the boundedness and compactness point of view. A characteristic feature of the monograph is that most of the statements proved here have the form of criteria. These criteria enable us, for example, togive var ious explicit examples of pairs of weighted Banach function spaces governing boundedness/compactness of a wide class of integral operators. The book has two main parts. The first part, consisting of Chapters 1-5, covers theinvestigation ofclassical operators: Hardy-type transforms, fractional integrals, potentials and maximal functions. Our main goal is to give a complete description of those Banach function spaces in which the above-mentioned operators act boundedly (com pactly). When a given operator is not bounded (compact), for example in some Lebesgue space, we look for weighted spaces where boundedness (compact ness) holds. We develop the ideas and the techniques for the derivation of appropriate conditions, in terms of weights, which are equivalent to bounded ness (compactness).

Author : Mark Aleksandrovich Krasnoselʹskiĭ
Publisher : Unknown
Page : 544 pages
File Size : 41,8 Mb
Release : 1976
Category : Mathematics
ISBN : UOM:39015049299624

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Integral Operators in Spaces of Summable Functions by Mark Aleksandrovich Krasnoselʹskiĭ Pdf

Author : Nihon Sūgakkai
Publisher : MIT Press
Page : 1180 pages
File Size : 45,9 Mb
Release : 1993
Category : Mathematics
ISBN : 0262590204

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Encyclopedic Dictionary of Mathematics by Nihon Sūgakkai Pdf

V.1. A.N. v.2. O.Z. Apendices and indexes.

Author : Alfredo Berm?dez
Publisher : SIAM
Page : 1062 pages
File Size : 47,7 Mb
Release : 2000-01-01
Category : Science
ISBN : 0898714702

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Fifth International Conference on Mathematical and Numerical Aspects of Wave Propagation by Alfredo Berm?dez Pdf

This conference was held in Santiago de Compostela, Spain, July 10-14, 2000. This volume contains papers presented at the conference covering a broad range of topics in theoretical and applied wave propagation in the general areas of acoustics, electromagnetism, and elasticity. Both direct and inverse problems are well represented. This volume, along with the three previous ones, presents a state-of-the-art primer for research in wave propagation. The conference is conducted by the Institut National de Recherche en Informatique et en Automatique with the cooperation of SIAM.

Author : M. Hazewinkel
Publisher : Springer
Page : 952 pages
File Size : 50,8 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9781489937933

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Encyclopaedia of Mathematics by M. Hazewinkel Pdf

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 525 pages
File Size : 52,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9789400959972

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Encyclopaedia of Mathematics by Michiel Hazewinkel Pdf

This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Author : Viktor G. Kravchenko,Georgii S. Litvinchuk
Publisher : Springer Science & Business Media
Page : 288 pages
File Size : 48,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401111805

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Introduction to the Theory of Singular Integral Operators with Shift by Viktor G. Kravchenko,Georgii S. Litvinchuk Pdf

This book is devoted to the Fredholm theory of singular integral operators with shift in Lp, 1

Author : Solomon G. Mikhlin,Siegfried Prößdorf
Publisher : Springer Science & Business Media
Page : 530 pages
File Size : 52,8 Mb
Release : 1987
Category : Mathematics
ISBN : 3540159673

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Singular Integral Operators by Solomon G. Mikhlin,Siegfried Prößdorf Pdf

The present edition differs from the original German one mainly in the following addi tional material: weighted norm inequalities for maximal functions and singular opera tors (§ 12, Chap. XI), polysingular integral operators and pseudo-differential operators (§§ 7, 8, Chap. XII), and spline approximation methods for solving singular integral equations (§ 4, Chap. XVII). Furthermore, we added two subsections on polynomial approximation methods for singular integral equations over an interval or with dis continuous coefficients (Nos. 3.6 and 3.7, Chap. XVII). In many places we incorporated new results which, in the vast majority, are from the last five years after publishing the German edition (note that the references are enlarged by about 150 new titles). S. G. Mikhlin wrote §§ 7, 8, Chap. XII, and the other additions were drawn up by S. Prossdorf. We wish to express our deepest gratitude to Dr. A. Bottcher and Dr. R. Lehmann who together translated the text into English carefully and with remarkable expertise.

Author : Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick
Publisher : American Mathematical Soc.
Page : 536 pages
File Size : 49,6 Mb
Release : 2019-09-03
Category : Dirichlet principle
ISBN : 9781470450823

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The Dirichlet Space and Related Function Spaces by Nicola Arcozzi,Richard Rochberg,Eric T. Sawyer,Brett D. Wick Pdf

The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.

Author : Michael Ruzhansky,Makhmud Sadybekov,Durvudkhan Suragan
Publisher : CRC Press
Page : 366 pages
File Size : 41,8 Mb
Release : 2020-02-07
Category : Mathematics
ISBN : 9780429780578

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Spectral Geometry of Partial Differential Operators by Michael Ruzhansky,Makhmud Sadybekov,Durvudkhan Suragan Pdf

The aim of Spectral Geometry of Partial Differential Operators is to provide a basic and self-contained introduction to the ideas underpinning spectral geometric inequalities arising in the theory of partial differential equations. Historically, one of the first inequalities of the spectral geometry was the minimization problem of the first eigenvalue of the Dirichlet Laplacian. Nowadays, this type of inequalities of spectral geometry have expanded to many other cases with number of applications in physics and other sciences. The main reason why the results are useful, beyond the intrinsic interest of geometric extremum problems, is that they produce a priori bounds for spectral invariants of (partial differential) operators on arbitrary domains. Features: Collects the ideas underpinning the inequalities of the spectral geometry, in both self-adjoint and non-self-adjoint operator theory, in a way accessible by anyone with a basic level of understanding of linear differential operators Aimed at theoretical as well as applied mathematicians, from a wide range of scientific fields, including acoustics, astronomy, MEMS, and other physical sciences Provides a step-by-step guide to the techniques of non-self-adjoint partial differential operators, and for the applications of such methods. Provides a self-contained coverage of the traditional and modern theories of linear partial differential operators, and does not require a previous background in operator theory.

Author : Alampallam V. Balakrishnan
Publisher : Springer Science & Business Media
Page : 385 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461258650

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Applied Functional Analysis by Alampallam V. Balakrishnan Pdf

In preparing the second edition, I have taken advantage of the opportunity to correct errors as well as revise the presentation in many places. New material has been included, in addition, reflecting relevant recent work. The help of many colleagues (and especially Professor J. Stoer) in ferreting out errors is gratefully acknowledged. I also owe special thanks to Professor v. Sazonov for many discussions on the white noise theory in Chapter 6. February, 1981 A. V. BALAKRISHNAN v Preface to the First Edition The title "Applied Functional Analysis" is intended to be short for "Functional analysis in a Hilbert space and certain of its applications," the applications being drawn mostly from areas variously referred to as system optimization or control systems or systems analysis. One of the signs of the times is a discernible tilt toward application in mathematics and conversely a greater level of mathematical sophistication in the application areas such as economics or system science, both spurred undoubtedly by the heightening pace of digital computer usage. This book is an entry into this twilight zone. The aspects of functional analysis treated here are rapidly becoming essential in the training at the advance graduate level of system scientists and/or mathematical economists. There are of course now available many excellent treatises on functional analysis.

Author : María Cristina Pereyra,Stefania Marcantognini,Alexander M. Stokolos,Wilfredo Urbina
Publisher : Springer
Page : 460 pages
File Size : 48,5 Mb
Release : 2017-07-10
Category : Mathematics
ISBN : 9783319515939

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Harmonic Analysis, Partial Differential Equations, Banach Spaces, and Operator Theory (Volume 2) by María Cristina Pereyra,Stefania Marcantognini,Alexander M. Stokolos,Wilfredo Urbina Pdf

This book is the second of a two volume series. Covering a range of subjects from operator theory and classical harmonic analysis to Banach space theory, this book features fully-refereed, high-quality papers exploring new results and trends in weighted norm inequalities, Schur-Agler class functions, complex analysis, dynamical systems, and dyadic harmonic analysis. Graduate students and researchers in analysis will find inspiration in the articles collected in this volume, which emphasize the remarkable connections between harmonic analysis and operator theory. A survey of the two weight problem for the Hilbert transform and an expository article on the Clark model to the case of non-singular measures and applications to the study of rank-one perturbations are included. The material for this volume is based on the 13th New Mexico Analysis Seminar held at the University of New Mexico, April 3-4, 2014 and on several special sections of the Western Spring Sectional Meeting at the University of New Mexico, April 4-6,2014. During the event, participants honored the memory of Cora Sadosky—a great mathematician who recently passed away and who made significant contributions to the field of harmonic analysis. Cora was an exceptional scientist and human being. She was a world expert in harmonic analysis and operator theory, publishing over fifty-five research papers and authoring a major textbook in the field. Participants of the conference include new and senior researchers, recent doctorates as well as leading experts in the area.