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Fundamental solutions of pseudodifferential equations connected with $p$-adic quadratic forms

A. N. Kochubei

Institute of Mathematics, Ukrainian National Academy of Sciences

Abstract: We construct and study fundamental solutions corresponding to certain classes of pseudodifferential operators with symbols of the form $|h(\xi )|_p^\alpha$, $\alpha>0$, where $h(\xi)$, $\xi=(\xi_1,\dots,\xi_n)$, is a non-degenerate $p$-adic quadratic form.

MSC: 26E30, 30G06

Received: 25.04.1997

DOI: 10.4213/im222

 English version: Izvestiya: Mathematics, 1998, 62:6, 1169–1188

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