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http://dx.doi.org/10.4134/CKMS.2005.20.4.657

GREEN FUNCTIONS ON THE p-ADIC VECTOR SPACE  

SON, JIN-Woo (Department of Mathematics Kyungnam University)
RIM, KYUNG-SOO (Department of Mathematics Sognag University)
Publication Information
Communications of the Korean Mathematical Society / v.20, no.4, 2005 , pp. 657-669 More about this Journal
Abstract
Calculations of some integrals on the n-dimensional vector space over $\mathbb{Q}_p$ are useful in getting some other formulations of quantum mechanics and the field theory of p-adic mathematical physics. For reasons of these, we estimate several integrals. As an application, we derive some properties for the p-adic Green functions.
Keywords
p-adic green function; p-adic Fourier transform; and series expansion of p-adic green function;
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1 W. Chong, M.-S. Kim, T. Kim, and J.-W. Son, On the p-adic spectral analysis and multiwavelet on $L^2$($Q^{n}_{p}$), Int. J. Math. Math. Sci. 2003 (2003), 2619-2633   DOI   ScienceOn
2 N. M. Chuong and N. V. Co, The multidimensional p-adic Green function, Proc. Amer. Math. Soc. 127 (1999), 685-694   DOI   ScienceOn
3 J. Igusa, An introduction to the theory of local zeta functions, AMS/IP Studies in Advanced Mathematics, 14, American Mathematical Society and International Press, 1994
4 A. N. Kochubei, On the asymptotics of p-adic Green functions, Proc. Steklov Inst. Math. 203 (1994), 105-113
5 A. N. Kochubei, Pseudo-differential equations and stochastics over non-Archi-medean fields, Monographs and Textbooks in Pure and Applied Mathematics, vol. 244, Marcel Dekker, Inc., New York, 2001
6 P. Sally and M. Taibleson, Special functions on locally compact fields, Acta Math. 116 (1966), 279-309   DOI
7 F. Sato, p-adic Green functions and zeta functions, Comment. Math. Univ. St. Pauli 51 (2002), 79-97
8 M. H. Taibleson, Fourier analysis on local fields, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1975
9 V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-Adic Analysis and Mathematical Physics, Series on Soviet & East European Mathematics, Vol. I, World Scientific, Singapore, 1994
10 A. Kh. Bikulov, Investigation of the p-adic Green function, Teoret. Mat. Fiz. (in Russian) 87 (1991), 376-390
11 A. N. Kochubei, On p-adic Green's functions, Theoret. and Math. Phys. 96 (1993), 854-865   DOI
12 Y. Jang, An asymptotic expansion of the p-adic Green function, Tohoku Math. J. 50 (1998), 229-242   DOI   ScienceOn