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Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Integral equations
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Bounded Integral Operators on L 2 Spaces (Paperback, Softcover reprint of the original 1st ed. 1978)
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Bounded Integral Operators on L 2 Spaces (Paperback, Softcover reprint of the original 1st ed. 1978)
Series: Ergebnisse der Mathematik und ihrer Grenzgebiete. 2. Folge, 96
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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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