By Jesus Araujo-gomez, Bertin Diarra, Alain Escassut

ISBN-10: 0821852914

ISBN-13: 9780821852910

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

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

Example text

As we cannot have a sequence of poles of f with strictly decreasing modules, the above process must stop at a certain rank, and this completes the proof of our assertion. Corollary 1: Suppose that, in Equation (E”), the polynomial A0 (X) is of the form aX m with a ∈ K \ {0} and m ∈ N . Then every solution f ∈ M(K) of Equation (E”) (with no pole at the origin) is an entire function. Proof: Indeed, such a solution cannot have non-zero poles, and hence is entire. Proof of Theorem 2: As indicated above, the whole problem is reduced to the s Ai (x)(σqi f )(x) = 0.

Khrennikov, Information dynamics in cognitive, psychological, social, and anomalous phenomena. : Fundamental Theories of Physics, Kluwer, Dordreht, 2004. [9] K. Mahler. p-adic numbers and their functions. Cambridge Univ. Press, 1981. (2nd edition). [10] W. H. Schikhof. Ultrametric calculus. An introduction to p-adic analysis. Cambridge University Press, Cambridge, 1984. I. Yurova, Van der Put basis and p-adic dynamics, p-Adic Numbers, Ultrametric Analysis, and Applications, 2(2), 2010, pp. 175-178 Institute for Information Security, Lomonosov Moscow State University, Michurinsky Prosp.

K¸akol and C. Perez-Garcia) Metrizability of compactoid sets in non-Archimedean Hausdorff (LM)-spaces. Ultrametric Functional Analysis (Nijmegen, 2002), 99-107, Contemp. , 319, Amer. Math. , Providence, RI, 2003. [65] (with C. Perez-Garcia) Strictness and closedness in p-Adic inductive limits. Ultrametric Functional Analysis (Aubi`ere, 2004), 79-100, Contemp. , 384, Amer. Math. , Providence, RI, 2005. [66] Sequence-spaces and applications. p-Adic Mathematical Physics, 206-213, AIP Conf. , 826, Amer.

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Advances in non-Archimedean Analysis: 11th International Conference P-adic Functional Analysis July 5-9, 2010 Universite Blaise Pascal, Clermont-ferrand, France by Jesus Araujo-gomez, Bertin Diarra, Alain Escassut

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