Non-radial functions, nonlocal operators and Markov processes over p-adic numbers
نویسندگان
چکیده
منابع مشابه
Parabolic Equations and Markov Processes Over p−adic Fields
In this paper we construct and study a fundamental solution of Cauchy’s problem for p−adic parabolic equations of the type ∂u (x, t) ∂t + (f (D, β)u) (x, t) = 0, x ∈ Qnp , n ≥ 1, t ∈ (0, T ] , where f (D, β), β > 0, is an elliptic pseudo-differential operator. We also show that the fundamental solution is the transition density of a Markov process with state space Qp .
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as one can check using induction on l. The usual absolute value function |x| satisfies these conditions with the ordinary triangle inequality (4). If N(x) = 0 when x = 0 and N(x) = 1 when x 6= 0, then N(x) satisfies these conditions with the ultrametric version of the triangle inequality. For each prime number p, the p-adic absolute value of a rational number x is denoted |x|p and defined by |x...
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ژورنال
عنوان ژورنال: Universitas Scientiarum
سال: 2019
ISSN: 2027-1352,0122-7483
DOI: 10.11144/javeriana.sc24-2.nrfn