Abstract:
We consider operators in L2(K), where K is a local field that is a sum
of the operator of convolution with a generalized function and multiplication by a function. A criterion of self-adjointness is given, and some results on the discrete spectrum are obtained. An analog of the Feynman–Kac formula is derived.
Citation:
R. S. Ismagilov, “Spectrum of a self-adjoint operator in L2(K), where K is a local field; analog of the Feynman–Kac formula”, TMF, 89:1 (1991), 18–24; Theoret. and Math. Phys., 89:1 (1991), 1024–1028
\Bibitem{Ism91}
\by R.~S.~Ismagilov
\paper Spectrum of a~self-adjoint operator in $L_2(K)$, where~$K$ is a local field; analog of the Feynman--Kac formula
\jour TMF
\yr 1991
\vol 89
\issue 1
\pages 18--24
\mathnet{http://mi.mathnet.ru/tmf5843}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1151367}
\zmath{https://zbmath.org/?q=an:0780.47038|0766.47028}
\transl
\jour Theoret. and Math. Phys.
\yr 1991
\vol 89
\issue 1
\pages 1024--1028
\crossref{https://doi.org/10.1007/BF01016802}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1991HT16100003}
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https://www.mathnet.ru/eng/tmf5843
https://www.mathnet.ru/eng/tmf/v89/i1/p18
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