Sait-Ametov M. Measures on the space of distributions over the field of p-adic numbers

Measures on the space of distributions over the field of p-adic numbers. Constructing and investigation of the measures on the functional space over the field of p-adic numbers. The methods of the non-Archimedean analisys, algebra and number theory, abstract harmonical analisys, theory of stochastic processes, mathematical physics. The investigation of an elliptic pseudo-differential operator over the field of p-adic numbers and its Green function was completed. A Gaussian measure on the space of distributions over the field of p-adic numbers was constructed. The support properties of the Gaussian measure was investigated. The Wick order of a distribution over the field of p-adic numbers was defined. A class of non-Gaussian measures over the field of p-adic numbers analogous to those describing polinomial interactions in Eucledean quantum field theory was constructed. The p-adic analogs of the Schwinger functions of the semi-Dirichlet states was defined and studied. The results obtained are new and canbe used in the further development of the infinitely-dimentional non-Archemedian analisys and p-adic mathematical physics.