Titlebook: Bounded Integral Operators on L 2 Spaces; Paul Richard Halmos,Viakalathur Shankar Sunder Book 1978 Springer-Verlag Berlin Heidelberg 1978

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Kernels, is the set of nonnegative real numbers, and H is the unit interval, i.e., the set of real numbers between 0 and 1 inclusive; in all these cases the measure is Lebesgue measure defined on the class of all Borei sets. This notation (including ., ., ., and .) will be fixed throughout.

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Boundedness,the domain of Int .. Another possibility: a kernel may or may not be closed. (Problem 3.12 can therefore be expressed this way: is it true that if dom . is closed, then . is closed?) A notational possibility for bounded kernels (that is hereby adopted): write ‖.‖ instead of ‖Int .‖.

FAR

Absolute Boundedness,value. These vague and heuristic comments lead to at least one specific and precise question: is it true that if . and .’ are kernels, .’ is bounded, and |.(., .)|≦|.’(., .)| almost everywhere, then . is bounded?

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Book 1978n") 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 th

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Inclement

Fluorescence Based Sensor Arrays,the domain of Int .. Another possibility: a kernel may or may not be closed. (Problem 3.12 can therefore be expressed this way: is it true that if dom . is closed, then . is closed?) A notational possibility for bounded kernels (that is hereby adopted): write ‖.‖ instead of ‖Int .‖.

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Energy transfer in concentrated systems,value. These vague and heuristic comments lead to at least one specific and precise question: is it true that if . and .’ are kernels, .’ is bounded, and |.(., .)|≦|.’(., .)| almost everywhere, then . is bounded?

Fillet,Filet

onstruction") 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 li

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