Ecuación de la onda plana en un espacio no- arquimediano con amortecimiento
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Abstract
El presente artículo, considera K un cuerpo local no- arquimediano, se muestra que para solucionar la ecuación de la onda plana sobre un espacio no arquimediano se considera una función de prueba f(t + w1x1 + w2x2 + … + wnxn) de valor complejo Bruhat – Schwartz en K, (t,x1,x2, …, xn) Є Kn+1, max|wi| = 1, que satisface para algún , para un cierta ecuación homogénea pseudo-diferencial, un análogo a la ecuación de la onda clásica, se desarrolla la teoría del problema de Cauchy para la ecuación de la onda plana sobre espacio no arquimediano.
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References
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Chernov, V. (1970). Homogeneous distributions and the Radon transform in the space of rectangular matrices over a continuous locally compact disconnected field. Soviet Math. Dokl, 415–418.
Cruz, H. (2018). Aplicación del Teorema de Hahn Banach No-Arquimediano: Una introducción a los Espacio Vectorial Normado No-Arquimediano. Epaña: Editorial Académica Española.
Eidelman, S., Ivasyshen, S. , and Kochubei, A. (2004). Analytic Methods in the Theory of Differential and Pseudo-Differential Equations of Parabolic Type. basel: Birkh¨auser.
Gelfand, I., Graev, M. & Piatetski-Shapiro, I. (1969). Representation Theory and Automorphic. Philadelphia: Saunders.
Helgason, S. (1980). The Radon Transform. boston: Brikhäuser.
Kochubei, A. (2001). Pseudo-Differential Equations and Stochastics over Non-Archimedean Fields. New York: Marcel Dekker.
Kochubei, A. (2009). On a p-adic waver equation. Proceedings of the Steklov Institute of Mathematics, 143-147. DOI:10.1134/S0081543809020138
Kozyrev, S. (2004). p-Adic pseudo-differential operators: methods and applications. Proceedings of the Steklov Institute of Mathematics, 138(3), 143–153. DOI: https://doi.org/10.4213/tmf31
Samko, S. (2001). Hypersingular Integrals and Their Applications. London: Taylor and Francis.
Schikhof, W. (1984). Ultrametric Calculus An Introduction to p-adic análisis. Cambrigde University Pres.
Schikhof, W. (2003). A Crash Course In p-Adic Analysis. Cambrigde University Pres.
Schneide, P. (2005). Nonarchimedean Fuctional Analysis. New York: Berlin-Heidel-Berg.
Taibleson, M. (1968). Harmonic analysis on n-dimensional vector spaces over local fields. I. Basic results on fractional integration. Mathematische Annalen, 176, 191–207. http://eudml.org/doc/161690
Vladimirov, V. (2003). Tables of Integrals of Complex-Valued Functions of p-Adic Arguments. Moscow: Steklov Mathematical Institute, 284(2), 3-88. DOI: https://doi.org/10.4213/spm5
Zuñiga, G. (2004). Pseudo-differential equations connected with p-adic forms and local zeta functions. Bulletin of the Australian Mathematical Society, 70(1), 73–86. DOI: https://doi.org/10.1017/S0004972700035838