p-Adic interpolation and approximation of a continuous function by linear combinations of shifts of p-adic valuations

p-ADIC INTERPOLATION

Although N is discrete in R, it is not discrete in Qp, and in fact has closure Zp. This raises the possibility of p-adically interpolating a sequence an, which is really a function n 7→ an on N, to a continuous function x 7→ ax with x ∈ Zp. Our basic question is this: when does a function f : N→ Qp extend to a continuous function Zp → Qp? We will look at some concrete examples, then see what a ...

P-adic Valuations and K-regular Sequences

Abstract A sequence is said to be k-automatic if the nth term of this sequence is generated by a finite state machine with n in base k as input. Regular sequences were first defined by Allouche and Shallit as a generalization of automatic sequences. Given a prime p and a polynomial f(x) ∈ Qp[x], we consider the sequence {vp(f(n))}n=0, where vp is the p-adic valuation. We show that this sequence...

p-adic Shearlets

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

Hensel’s lemma, valuations, and p-adic numbers

The Eisenstein Measure and P-Adic Interpolation

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