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Sibirskii Matematicheskii Zhurnal, 2008, Volume 49, Number 5, Pages 1083–1086 (Mi smj1905)  
On the functions of one selfadjoint integral operator

V. B. Korotkov

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
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Abstract: We construct a selfadjoint Akhiezer integral operator $S$ on $L_2(-1,1)$ with the spectrum $\{-1;0;1\}$ and the property that every function $\varphi(S)$ that is not a multiple of $S$ fails to be an Akhiezer integral operator.
Keywords: Akhiezer integral operator, function of a selfadjoint operator, spectral function.
Received: 16.01.2007
English version:
Siberian Mathematical Journal, 2008, Volume 49, Issue 5, Pages 857–859
DOI: https://doi.org/10.1007/s11202-008-0085-x
Bibliographic databases:
UDC: 517.983
Language: Russian
Citation: V. B. Korotkov, “On the functions of one selfadjoint integral operator”, Sibirsk. Mat. Zh., 49:5 (2008), 1083–1086; Siberian Math. J., 49:5 (2008), 857–859
Citation in format AMSBIB
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