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TMF, 2014, Volume 180, Number 1, Pages 3–9 (Mi tmf8638)  

Asymptotic form of the spectrum of operators associated with $p$-adic fields

R. S. Ismagilov

Bauman Moscow State University for Technology, Moscow, Russia

Abstract: We consider a locally compact nonconnected nondiscrete field and study a linear operator given by the sum of the operator of multiplication by a function and the operator of convolution with a generalized function. We derive the asymptotic form of the spectrum of that linear operator. In this problem, we use the generalized $p$-adic Feynman–Kac formula.

Keywords: asymptotic form, spectrum, Feynman–Kac formula, operator trace, $p$-adic field

DOI: https://doi.org/10.4213/tmf8638

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English version:
Theoretical and Mathematical Physics, 2014, 180:1, 753–758

Bibliographic databases:

Received: 06.01.2014

Citation: R. S. Ismagilov, “Asymptotic form of the spectrum of operators associated with $p$-adic fields”, TMF, 180:1 (2014), 3–9; Theoret. and Math. Phys., 180:1 (2014), 753–758

Citation in format AMSBIB
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\paper Asymptotic form of the~spectrum of operators associated with $p$-adic fields
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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