Hilbert-Schmidt integral operator
- Hilbert-Schmidt integral operator
In mathematics, a Hilbert-Schmidt integral operator is a type of integral transform. Specifically, given a domain (an open and connected set) Ω in "n"-dimensional Euclidean space R"n", a Hilbert-Schmidt kernel is a function "k" : Ω × Ω → C with
:
and the associated Hilbert-Schmidt integral operator is the operator "K" : "L"2(Ω; C) → "L"2(Ω; C) given by
:
Hilbert-Schmidt integral operators are both continuous (and hence bounded) and compact.
See also
* Hilbert-Schmidt operator
References
* cite book
author = Renardy, Michael and Rogers, Robert C.
title = An introduction to partial differential equations
series = Texts in Applied Mathematics 13
edition = Second edition
publisher = Springer-Verlag
location = New York
year = 2004
pages = 356
isbn = 0-387-00444-0 (Sections 7.1 and 7.5)
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