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Analytic potential theory over the p -adics

Shai Haran — 1993

Annales de l'institut Fourier

Over a non-archimedean local field the absolute value, raised to any positive power α > 0 , is a negative definite function and generates (the analogue of) the symmetric stable process. For α ( 0 , 1 ) , this process is transient with potential operator given by M. Riesz’ kernel. We develop this potential theory purely analytically and in an explicit manner, obtaining special features afforded by the non-archimedean setting ; e.g. Harnack’s inequality becomes an equality.

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