Bounded Integral Operators on L 2 Spaces (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 96)

Halmos, P. R. Richard; Sunder, V. S.

ISBN 10: 3642670180 ISBN 13: 9783642670183

Editorial: Springer, 2011

Idioma: Ingl�s

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T�tulo

Bounded Integral Operators on L 2 Spaces (Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 96)

Editor

Springer

Fecha de publicaci�n

2011

Idioma

Ingl�s

ISBN 10

3642670180

ISBN 13

9783642670183

Encuadernaci�n

Encuadernaci�n de tapa blanda

Estado

New

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Sinopsis

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.

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