By Jesus Araujo-gomez, Bertin Diarra, Alain Escassut

This quantity includes papers in line with lectures given on the 11th overseas convention on $p$-adic sensible research, which used to be held from July 5-9, 2010, in Clermont-Ferrand, France. The articles accumulated right here characteristic fresh advancements in a variety of components of non-Archimedean research: Hilbert and Banach areas, finite dimensional areas, topological vector areas and operator idea, strict topologies, areas of constant features and of strictly differentiable services, isomorphisms among Banach features 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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**Additional resources 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**

McKennon in 1980, assures that every inductive sequence of real or complex reﬂexive Banach spaces is regular. However, in the non-Archimedean case, the validity of this result depends on the ground ﬁeld. In fact, Nicole and C. Perez-Garcia proved in [69] that it remains true for inductive limits of Banach spaces over spherically complete ﬁelds but fails when spherical completeness is dropped. REMEMBERING NICOLE DE GRANDE-DE KIMPE 1936-2008 REMEMBERING NICOLE DE GRANDE-DE KIMPE 1936-2008 25 The above distinction between spherically and non-spherically complete ﬁelds, for inductive limits of Banach spaces, does not matter when the steps are Fr´echet spaces.

Y. Khrennikov in [52] and in the study of the p-Adic probability theory carried out by Nicole, S. Albeverio, R. Y. Khrennikov in [59]. IV. (Spaces of diﬀerentiable functions) Assume K ⊃ Qp . If in Example II we take bkn = nk , we have that K(B)× is linearly homeomorphic to the strong dual of the Fr´echet space of inﬁnitely diﬀerentiable K-valued functions on Zp . Y. Khrennikov and L. van Hamme. They called K(B)× the space of distributions. 13. p-Adic inductive limits play also a central role in the theory of diﬀerential equations and of the Monsky-Washnitzer cohomology in p-Adic Analysis, as it was shown in various works by G.

Perez-Garcia) On compactoids in (LB)-spaces. Bull. Polish Acad. Sci. Math. 45 (1997), 313-321. [57] (with J. Aguayo and S. Navarro) Strict topologies and duals in spaces of functions. p-Adic Functional Analysis (Pozna´ n, 1998), 1-10, Lecture Notes in Pure and Appl. , 207, Dekker, New York, 1999. Y. Khrennikov and L. van Hamme) The Fourier transform for p-Adic tempered distributions. p-Adic Functional Analysis (Pozna´ n, 1998), 97-112, Lecture Notes in Pure and Appl. , 207, Dekker, New York, 1999.