Abstract:
Vladimirov's methods for computing Gaussian integrals and constructing eigenfunctions of a fractional differentiation operator over the field of $p$-adic numbers is extended to the case of an arbitrary local field with a discrete valuation and characteristic of the residue field different from 2.
\Bibitem{Koc94}
\by A.~N.~Kochubei
\paper Gaussian integrals and spectral theory over a~local field
\jour Russian Acad. Sci. Izv. Math.
\yr 1995
\vol 45
\issue 3
\pages 495--503
\mathnet{http://mi.mathnet.ru/eng/im524}
\crossref{https://doi.org/10.1070/IM1995v045n03ABEH001668}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1317209}
\zmath{https://zbmath.org/?q=an:0852.46061}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TW91000003}
Linking options:
https://www.mathnet.ru/eng/im524
https://doi.org/10.1070/IM1995v045n03ABEH001668
https://www.mathnet.ru/eng/im/v58/i6/p69
This publication is cited in the following 4 articles:
Jawad Ettayb, “On the operator equations ABA = A
2 and BAB = B
2 on non-Archimedean Banach spaces”, Topological Algebra and its Applications, 11:1 (2023)
V. S. Vladimirov, “Tables of Integrals of Complex-Valued Functions of $p$-Adic Arguments”, Proc. Steklov Inst. Math., 284, suppl. 2 (2014), S1–S59
Pseudo-Differential Equations And Stochastics Over Non-Archimedean Fields, 2001
A. Kh. Bikulov, I. V. Volovich, “$p$-adic Brownian motion”, Izv. Math., 61:3 (1997), 537–552
Citation in format AMSBIB
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