Resumen Presentamos una base de wavelets p-ádica para espacios de tipo Sobolev que consiste de vectores propios de ciertos operadores pseudodiferenciales. Nuestro resultado extiende un conocido resultado debido a S. Kozyrev.

Abstract We present a basis of p-adic wavelets for Sobolev-type spaces consisting of eigenvectors of certain pseudodifferential operators. Our result extends a well-known result due to S. Kozyrev.

Abstract In this paper, we investigate p-adic q-integral (q-Volkenborn integral) on Z p of p-adic gamma function via their Mahler expansions. We also derived two q-Volkenborn integrals of p-adic gamma function in terms of q-Daehee polynomials and numbers and q-Daehee polynomials and numbers of the second kind. Moreover, we discover q-Volkenborn integral of the derivative of p-adic gamma function. We acquire the relationship between the p-adic gamma function and Stirling numbers of the first kind. We finally develop a novel and interesting representation for the p-adic Euler constant by means of the q-Daehee polynomials and numbers.

En este artículo estudiamos el problema del primer retorno asociado a un operador seudodiferencial elíptico con símbolo no radial de dimensión 3 sobre el cuerpo de los números p-ádicos

In this article we study the problem of first return associated to an elliptic pseudodifferential operator with non-radial symbol of dimension 3 over the p-adics

En este artículo se estudia el problema del primer retorno asociado a ciertos operadores pseudo-diferenciales elípticos en dimensiones 4 y 2 sobre los números p-ádicos. Este tipo de problemas está conectado con ciertos modelos de sistemas complejos.

In this article we study the problem of the first passage time associated to certain elliptic pseudodifferential operators in dimensions 4 and 2 over the p-adics. This type of problems appeared in connection with certain models of complex systems.

We prove that for any prime p and any integer k > 2, there exist in the ring Zp of p-adic integers arbitrarily long sequences whose sequence of k-th powers 1) has its k-th difference sequence equal to the constant sequence (k!); and 2) is not a sequence of consecutive k-th powers. This shows that the analogue of Buchi's problem for higher powers has a negative answer over Zp. This result for k = 2 was recently obtained by J. Browkin.

En este artículo se estudia la existencia y unicidad de soluciones del problema de Cauchy asociado a un tipo general de ecuación parabólica p-ádica, construida usando el operador de Taibleson. Los resultados presentados aquí constituyen una extensión de algunos de los resultados obtenidos por Zúñiga-Galindo y el autor en [13].

In this paper we study the existence and uniqueness of the Cauchy problem for a general type of p-adic parabolic pseudo-differential operators constructed using the Taibleson operator. The results presented here constitute an extension of some results obtained by Zúñiga-Galindo and the author [13].