Estimates of singular numbers of a Hilbert-Schmidt integral operator (Q690792)
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scientific article; zbMATH DE number 6110990
| Language | Label | Description | Also known as |
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| English | Estimates of singular numbers of a Hilbert-Schmidt integral operator |
scientific article; zbMATH DE number 6110990 |
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Estimates of singular numbers of a Hilbert-Schmidt integral operator (English)
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29 November 2012
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Given an integral operator in \(L_2[0,1]\) with a Hilbert-Schmidt kernel, the author provides estimates for its singular numbers in terms of the continuity moduli of its kernel. This yields sharpenings of classical results due to I.\ Fredholm and M. G.\ Krein, respectively. The proofs are based on ideas taken from [\textit{P. L.\ Ul'yanov},\ Mat.\ Sb.\ 81, 104--131 (1970; Zbl 0215.17702)].
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singular numbers
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Hilbert-Schmidt integral operators
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continuity modulus of the kernel
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