Riesz kernels and pseudodifferential operators attached to quadratic forms over p-adic fields |
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| Authors: | O Casas-Sánchez W A Zúñiga-Galindo |
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| Institution: | 1. Departamento de Matemáticas Ciudad Universitaria, Universidad Nacional de Colombia, Bogotá D.C., Colombia
2. Departamento de Matemáticas, Unidad Querétaro, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Libramiento Norponiente #2000, Fracc. Real de Juriquilla, Santiago de Querétaro, Qro., 76230, México
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| Abstract: | We study pseudodifferential equations and Riesz kernels attached to certain quadratic forms over p-adic fields. We attach to an elliptic quadratic form of dimension two or four a family of distributions depending on a complex parameter, the Riesz kernels, and show that these distributions form an Abelian group under convolution. This result implies the existence of fundamental solutions for certain pseudodifferential equations like in the classical case. |
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