Geodesic
Spectrum of a~self-adjoint operator in $L_2(K)$, where~$K$ is a local field; analog of the Feynman--Kac formula
Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 18-24

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We consider operators in $L_2(K)$, 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. 
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     author = {R. S. Ismagilov},
     title = {Spectrum of a~self-adjoint operator in $L_2(K)$, where~$K$ is a local field; analog of the {Feynman--Kac} formula},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {18--24},
     publisher = {mathdoc},
     volume = {89},
     number = {1},
     year = {1991},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a2/}
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R. S. Ismagilov. Spectrum of a~self-adjoint operator in $L_2(K)$, where~$K$ is a local field; analog of the Feynman--Kac formula. Teoretičeskaâ i matematičeskaâ fizika, Tome 89 (1991) no. 1, pp. 18-24. http://geodesic.mathdoc.fr/item/TMF_1991_89_1_a2/