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2013

A Survey on Reproducing Kernel Krein Spaces

Gheondea, Aurelian

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This is a survey on reproducing kernel Krein spaces and their interplay with operator valued Hermitian kernels.

Existence and uniqueness properties are carefully reviewed.
The approach we follow in this survey uses a more abstract but very useful concept of linearization or Kolmogorov decomposition, as well as the underlying concept of Krein space induced by a selfadjoint operator and that of Krein space continuously embedded.
The operator range feature of reproducing kernel spaces is emphasized.

A Survey on Reproducing Kernel Krein Spaces · Around

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S. Zaremba
1907
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J. Mercer
1909
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G. Szegö
1921
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S. Bergman
1922
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S. Bochner
1922
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E.H. Moore
1939
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A.N. Kolmogorov
1941
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M.A. Naĭmark
1943
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V.P. Potapov
1955
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1955
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L. Schwartz
1964
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P.L. Duren
1970
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P. Koosis
1970
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