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Author : Irwin E. Schochetman
Publisher : Unknown
Page : 0 pages
File Size : 46,9 Mb
Release : 1978
Category : Banach spaces
ISBN : LCCN:75004580
Author : Irwin E. Schochetman
Publisher : American Mathematical Soc.
Page : 120 pages
File Size : 51,6 Mb
Release : 1978
Category : Banach spaces
ISBN : 9780821822029
Author : Irwin E. Schochetman
Publisher : American Mathematical Soc.
Page : 53 pages
File Size : 48,7 Mb
Release : 1978
Category : Integral operators
ISBN : 9780821822074
Author : A.G. Kusraev
Publisher : Springer Science & Business Media
Page : 456 pages
File Size : 40,7 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9789401593496
The notion of a dominated or rnajorized operator rests on a simple idea that goes as far back as the Cauchy method of majorants. Loosely speaking, the idea can be expressed as follows. If an operator (equation) under study is dominated by another operator (equation), called a dominant or majorant, then the properties of the latter have a substantial influence on the properties of the former . Thus, operators or equations that have "nice" dominants must possess "nice" properties. In other words, an operator with a somehow qualified dominant must be qualified itself. Mathematical tools, putting the idea of domination into a natural and complete form, were suggested by L. V. Kantorovich in 1935-36. He introduced the funda mental notion of a vector space normed by elements of a vector lattice and that of a linear operator between such spaces which is dominated by a positive linear or monotone sublinear operator. He also applied these notions to solving functional equations. In the succeedingyears many authors studied various particular cases of lattice normed spaces and different classes of dominated operators. However, research was performed within and in the spirit of the theory of vector and normed lattices. So, it is not an exaggeration to say that dominated operators, as independent objects of investigation, were beyond the reach of specialists for half a century. As a consequence, the most important structural properties and some interesting applications of dominated operators have become available since recently.
Author : P. R. Halmos,V. S. Sunder
Publisher : Springer Science & Business Media
Page : 147 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642670169
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 : Semën Samsonovich Kutateladze
Publisher : Springer Science & Business Media
Page : 312 pages
File Size : 41,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401143059
Nonstandard methods of analysis consist generally in comparative study of two interpretations of a mathematical claim or construction given as a formal symbolic expression by means of two different set-theoretic models: one, a "standard" model and the other, a "nonstandard" model. The second half of the twentieth century is a period of significant progress in these methods and their rapid development in a few directions. The first of the latter appears often under the name coined by its inventor, A. Robinson. This memorable but slightly presumptuous and defiant term, non standard analysis, often swaps places with the term Robinsonian or classical non standard analysis. The characteristic feature of Robinsonian analysis is a frequent usage of many controversial concepts appealing to the actual infinitely small and infinitely large quantities that have resided happily in natural sciences from ancient times but were strictly forbidden in modern mathematics for many decades. The present-day achievements revive the forgotten term infinitesimal analysis which reminds us expressively of the heroic bygones of Calculus. Infinitesimal analysis expands rapidly, bringing about radical reconsideration of the general conceptual system of mathematics. The principal reasons for this progress are twofold. Firstly, infinitesimal analysis provides us with a novel under standing for the method of indivisibles rooted deeply in the mathematical classics.
Author : Anonim
Publisher : Unknown
Page : 652 pages
File Size : 48,5 Mb
Release : 1989
Category : Operator theory
ISBN : UCAL:B4342798
Author : Mark Aleksandrovich Krasnoselʹskiĭ
Publisher : Unknown
Page : 544 pages
File Size : 54,8 Mb
Release : 1976
Category : Mathematics
ISBN : UOM:39015049299624
Author : Library of Congress
Publisher : Unknown
Page : 1044 pages
File Size : 44,6 Mb
Release : 2024-06-28
Category : Electronic
ISBN : WISC:89126008374
Author : Albrecht Pietsch
Publisher : Springer Science & Business Media
Page : 855 pages
File Size : 53,9 Mb
Release : 2007-12-31
Category : Mathematics
ISBN : 9780817645960
Written by a distinguished specialist in functional analysis, this book presents a comprehensive treatment of the history of Banach spaces and (abstract bounded) linear operators. Banach space theory is presented as a part of a broad mathematics context, using tools from such areas as set theory, topology, algebra, combinatorics, probability theory, logic, etc. Equal emphasis is given to both spaces and operators. The book may serve as a reference for researchers and as an introduction for graduate students who want to learn Banach space theory with some historical flavor.
Author : S. Okada,Werner J. Ricker,Enrique A. Sánchez Pérez
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 53,9 Mb
Release : 2008-09-09
Category : Mathematics
ISBN : 9783764386481
This book deals with the analysis of linear operators from a quasi-Banach function space into a Banach space. The central theme is to extend the operator to as large a (function) space as possible, its optimal domain, and to take advantage of this in analyzing the original operator. Most of the material appears in print for the first time. The book has an interdisciplinary character and is aimed at graduates, postgraduates, and researchers in modern operator theory.
Author : American Mathematical Society
Publisher : Unknown
Page : 142 pages
File Size : 42,7 Mb
Release : 1985
Category : Mathematics
ISBN : CORNELL:31924051175101
Author : Ramon E Moore,Michael J Cloud
Publisher : Elsevier
Page : 193 pages
File Size : 46,5 Mb
Release : 2007-06-01
Category : Technology & Engineering
ISBN : 9780857099433
This course text fills a gap for first-year graduate-level students reading applied functional analysis or advanced engineering analysis and modern control theory. Containing 100 problem-exercises, answers, and tutorial hints, the first edition is often cited as a standard reference. Making a unique contribution to numerical analysis for operator equations, it introduces interval analysis into the mainstream of computational functional analysis, and discusses the elegant techniques for reproducing Kernel Hilbert spaces. There is discussion of a successful ‘‘hybrid’’ method for difficult real-life problems, with a balance between coverage of linear and non-linear operator equations. The authors successful teaching philosophy: ‘‘We learn by doing’’ is reflected throughout the book. Contains 100 problem-exercises, answers and tutorial hints for students reading applied functional analysis Introduces interval analysis into the mainstream of computational functional analysis
Author : Aref Jeribi
Publisher : Walter de Gruyter GmbH & Co KG
Page : 421 pages
File Size : 47,9 Mb
Release : 2018-03-19
Category : Mathematics
ISBN : 9783110492408
This book is devoted to recent developments concerning linear operators, covering topics such as the Cauchy problem, Riesz basis, frames, spectral theory and applications to the Gribov operator in Bargmann space. Also, integral and integro-differential equations as well as applications to problems in mathematical physics and mechanics are discussed. Contents Introduction Linear operators Basic notations and results Bases Semi-groups Discrete operator and denseness of the generalized eigenvectors Frames in Hilbert spaces Summability of series ν-convergence operators Γ-hypercyclic set of linear operators Analytic operators in Béla Szökefalvi-Nagy’s sense Bases of the perturbed operator T(ε) Frame of the perturbed operator T(ε) Perturbation method for sound radiation by a vibrating plate in a light fluid Applications to mathematical models Reggeon field theory
Author : Library of Congress
Publisher : Unknown
Page : 888 pages
File Size : 52,8 Mb
Release : 2024-06-28
Category : Monographic series
ISBN : WISC:89126009349
