We develop the basic theory of the Weyl symbolic calculus of pseudodifferential operators over the -adic numbers. We apply this theory to the study of elliptic operators over the -adic numbers and determine their asymptotic spectral behavior.
In this paper we prove microlocal version of the equidistribution theorem for Wigner distributions associated to Eisenstein series on . This generalizes a recent result of W. Luo and P. Sarnak who proves equidistribution for . The averaged versions of these results have been proven by Zelditch for an arbitrary finite-volume surface, but our proof depends essentially on the presence of Hecke operators and works only for congruence subgroups of . In the proof the key estimates come from applying...
It is proved that every real metrizable locally convex space which is not nuclear contains a closed additive subgroup K such that the quotient group G = (span K)/K admits a non-trivial continuous positive definite function, but no non-trivial continuous character. Consequently, G cannot satisfy any form of the Bochner theorem.
On considère l’espace où et sont deux fonctions définies-négatives, réelles et continues sur . On étudie la possibilité d’approcher, au sens de la norme de , tout élément de par des combinaisons linéaires d’éléments de qui sont transformés de Fourier de mesures positives de support inclus dans le spectre de . Des méthodes de théorie du potentiel permettent de donner une réponse positive (sous certaines hypothèses additionnelles). On obtient ainsi des généralisations, au cas de ,...