A Non-Archimedean Wave Equation

Details A Non-Archimedean Wave Equation A Non-Archimedean Wave Equation

2007-07-18

arxiv.org/abs/0707.2653v2

Mathematics

Number Theory

17 pages; the final version, to appear in Pacif. J. Math

Scientific paper

Let K be a non-Archimedean local field with the normalized absolute value $|\cdot |$. It is shown that a ``plane wave'' $f(t+\omega_1 x_1+... +\omega_nx_n)$, where f is a Bruhat-Schwartz complex-valued test function on K, $(t,x_1,..., x_n)\in K^{n+1}$, $\max\limits_{1\le j\le n}|\omega_j|=1$, satisfies, for any f, a certain homogeneous pseudo-differential equation, an analog of the classical wave equation. A theory of the Cauchy problem for this equation is developed.

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