Download Advances in P-adic and Non-archimedean Analysis: Tenth by Martin Berz, Khodr Shamseddine PDF

By Martin Berz, Khodr Shamseddine

This quantity comprises the court cases of the 10th overseas convention on p-adic and Non-Archimedean research, held at Michigan country collage in East Lansing, Michigan, on June 30-July three, 2008. This quantity additionally encompasses a kaleidoscope of papers in line with numerous of the extra vital talks awarded on the assembly. It offers a state-of-the-art connection to a few of crucial fresh advancements within the box. via a mix of survey papers, study articles, and wide references to previous paintings, this quantity permits the reader to speedy achieve an outline of present task within the box and develop into familiar with a few of the contemporary sub-branches of its improvement

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Additional resources for Advances in P-adic and Non-archimedean Analysis: Tenth International Conference June 30-july 3, 2008 Michigan State University East Lansing, Michigan

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In [10] it is shown that ψ has a unique continuation to A defined in the same way as ψ(f ) = ϕF (f ) ∀f ∈ A. Theorem 28: Let ψ ∈ M ult(A, . ) satisfy ψ(P ) = ϕF (P ) ∀P ∈ K[x], with F a circular filter on D of diameter r < 1. Then ψ(f ) = ϕF (f ) ∀f ∈ A. Consequently, all multiplicative norms whose restrictions to polynomials are not the Gauss norm . are defined by the circular filters on D of diameter < 1 and therefore the problem of characterizing continuous multiplicative norms of A only concerns the various continuations of the Gauss norm to A.

N≥0 n(n−1) |γn | and γn = (q − 1)n q 2 = sup n |q − 1| n≥0 (Ψn,q )(0). 3. The q-difference operators . − • − Let us consider for a ∈ Λ and f ∈ K{X} the formal power series ha (f )(X) = f (aX). It is clear that ha (f )(X) is a restricted power series and one obtains a continuous algebra endomorphism ha of K{X}, called a dilatation or a homothety operator, such that ha (1) = 1 and ha = 1. If |a| = 1, one sees that ha is a bijective isometry with reciprocical h−1 a = ha−1 . − • •− Let as above q ∈ K be such that |q| = 1, and that is not a root of unit.

Any shift-invariant operator u ∈ Endcom (K{X}) can be ex(n) ∆q , with γn = u(Ψn,q )(0) γn panded as a unique strongly convergent series u = [n]q ! and u = sup |γn |. n≥0 n≥0 SUBALGEBRAS OF BOUNDED LINEAR OPERATORS ONalgebra TATE ALGEBRA Subalgebras of bounded linear operators on Tate 21 9 4. The Jackson q-derivative and the q-difference operators In the first two subsections of this section, we assume only that K is an ultrametric complete valued field and we suppose that q is a unit of K that is not a root of unit ( for instance, if K is an extension of Qp any element q of K such that 1 |q − 1| < |p| p−1 is not a root of unit).

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