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A note on some expansions of p-adic functions

Grzegorz Szkibiel (1992)

Acta Arithmetica

Introduction. Recently J. Rutkowski (see [3]) has defined the p-adic analogue of the Walsh system, which we shall denote by ( ϕ ) m . The system ( ϕ ) m is defined in the space C(ℤₚ,ℂₚ) of ℂₚ-valued continuous functions on ℤₚ. J. Rutkowski has also considered some questions concerning expansions of functions from C(ℤₚ,ℂₚ) with respect to ( ϕ ) m . This paper is a remark to Rutkowski’s paper. We define another system ( h ) n in C(ℤₚ,ℂₚ), investigate its properties and compare it to the system defined by Rutkowski. The system...

A representation theorem for a class of rigid analytic functions

Victor Alexandru, Nicolae Popescu, Alexandru Zaharescu (2003)

Journal de théorie des nombres de Bordeaux

Let p be a prime number, p the field of p -adic numbers and p the completion of the algebraic closure of p . In this paper we obtain a representation theorem for rigid analytic functions on 𝐏 1 ( p ) C ( t , ϵ ) which are equivariant with respect to the Galois group G = G a l c o n t ( p / p ) , where t is a lipschitzian element of p and C ( t , ϵ ) denotes the ϵ -neighborhood of the G -orbit of t .

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