Local zeta functions and fundamental solutions for pseudo-differential operators over <Emphasis Type="Italic">p</Emphasis>-adic fields |
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Authors: | W A Zúñiga-Galindo |
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Institution: | 1.Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional Departamento de Matemáticas-Unidad Querétaro Libramiento Norponiente #2000,Fracc. Real de Juriquilla,Santiago de Querétaro, Qro.,México |
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Abstract: | We review the proof of the existence of a fundamental solution for a pseudo-differential operator with polynomial symbol based on the existence of a meromorphic continuation for the local zeta function attached to the symbol. We compute fundamental solutions for quasielliptic and Schrödinger-type pseudo-differential operators. As an application we solve certain initial value problems for Schrödinger-type pseudo-differential equations. We pose several questions and problems about the connection between local zeta functions and pseudo-differential operators. |
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