By Jesus Araujo-gomez, Bertin Diarra, Alain Escassut

ISBN-10: 0821852914

ISBN-13: 9780821852910

This quantity includes papers in accordance with lectures given on the 11th foreign convention on $p$-adic useful research, which used to be held from July 5-9, 2010, in Clermont-Ferrand, France. The articles amassed the following function fresh advancements in a variety of parts of non-Archimedean research: Hilbert and Banach areas, finite dimensional areas, topological vector areas and operator idea, strict topologies, areas of continuing capabilities and of strictly differentiable capabilities, isomorphisms among Banach features areas, and degree and integration. different themes mentioned during this quantity contain $p$-adic differential and $q$-difference equations, rational and non-Archimedean analytic capabilities, the spectrum of a few algebras of analytic capabilities, and maximal beliefs of the ultrametric corona algebra

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**Extra resources for Advances in non-Archimedean Analysis: 11th International Conference P-adic Functional Analysis July 5-9, 2010 Universite Blaise Pascal, Clermont-ferrand, France**

**Sample text**

Hence, (1) B0 = 1 ≡ 1 (mod 2), B0 + B1 = 1 + 2 = 3 ≡ 3 (mod 4); (2) |Bm |2 = 2n−1 (2n − 1) 2 = 2−(n−1) if 2n−1 ≤ m < 2n − 1 and n ≥ 2; 37 5 VAN DER PUT BASIS AND ERGODICITY OF 2-ADIC FUNCTIONS (3) 2n −1 m=2n−1 (Bm 2n−1 = 2 − 2n−1 ) · (n − 1) 2 2n −1 n−1 (2n m=2n−1 (2 = 2 −(n+1) ≤2 − 1) − 2n−1 ) = 2 . 4, the function f is ergodic. The proof for the next example goes along similar lines. Note however that in a contrast to the example considered before, coeﬃcients of δi (x) in the corresponding series depend on x now.

As (X) are constant. We will see that in this case every meromorphic solution f of the equation (E) is a rational function. , As (X) are constant. Then every non constant solution of Equation (E) in M(K) is a rational function having at most one pole α = 0. , As (X) are not all constant. Does this equation admit non rational solutions f ∈ M(K)? and what can we say about the order of growth of such a solution. Example 1: let q ∈ K, 0 < |q| < 1 and consider the so called Tschakaloﬀ function n(n−1) Tq (x) = q 2 xn .

Finally, we showed in [55] that (E, τ ), being an inductive limit of Banach spaces, is barrelled, and that (E, ) is polarly barrelled but not barrelled. H. Schikhof in 1986 about the existence of polarly barrelled spaces that are not barrelled when K is not spherically complete. II), with an adequate choice of the matrix B. Strictness of p-Adic inductive sequences was one of the favourite subjects of Nicole. (En )n is called strict if τn+1 |En = τn for all n. 24 C. H. SCHIKHOF In [65] Nicole and C.