Displaying similar documents to “Electrostatic fields due to distributions of electrons”

Analytic potential theory over the p -adics

Shai Haran (1993)

Annales de l'institut Fourier

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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.

Zero distributions via orthogonality

Laurent Baratchart, Reinhold Küstner, Vilmos Totik (2005)

Annales de l’institut Fourier

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We develop a new method to prove asymptotic zero distribution for different kinds of orthogonal polynomials. The method directly uses the orthogonality relations. We illustrate the procedure in four cases: classical orthogonality, non-Hermitian orthogonality, orthogonality in rational approximation of Markov functions and its non- Hermitian variant.