By Jesus Araujo-gomez, Bertin Diarra, Alain Escassut

ISBN-10: 0821852914

ISBN-13: 9780821852910

This quantity includes papers in keeping with 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 amassed right here function contemporary 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 services and of strictly differentiable services, isomorphisms among Banach services areas, and degree and integration. different issues mentioned during this quantity comprise $p$-adic differential and $q$-difference equations, rational and non-Archimedean analytic features, the spectrum of a few algebras of analytic features, and maximal beliefs of the ultrametric corona algebra

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Indag. Math. 38 (1976), 307-312. [21] Structure theorems for locally K-convex spaces. Indag. Math. 39 (1977), 11-22. B. Robinson) Compact maps and embeddings from an inﬁnite type power series space to a ﬁnite type power series space. J. Reine Angew. Math. 293/294 (1977), 52-61. [23] Locally convex spaces for which L(E) = L[E] and the Dvoretsky-Rogers theorem. Compositio Math. 35 (1977), 139-145. [24] Criteria for nuclearity in terms of generalized sequence spaces. Arch. Math. (Basel) 28 (1977), 644-651.

In particular, every closed bounded subset of E is complete, metrizable and compactoid. (iv) E is complete. (v) (En )n is regular. 17). 26 C. H. e. for each sequence x1 , x2 , . . tending to 0 in E there exists a sequence μ1 , μ2 , . . in K with limm |μm | = ∞ such that μ1 x1 , μ2 x2 , . . tends to 0 in E). (viii) Eb is Fr´echet. (ix) E and Eb are strictly of countable type, Montel (hence reﬂexive) and nuclear. In particular, E is the strong dual of the Fr´echet space Eb . 16. Since E is strictly of countable type (see (ix)), it is polar.

9], [10], [11], [13]). Here we mean to generalize some of the results obtained in Cl to meromorphic functions in a ultrametric ﬁeld. As in the complex case, our method is based upon the Nevanlinna Theory and follows closely some of the approachs used in the article [9]. Let us ﬁrst recall some basic notions of the ultrametric Nevanlinna Theory. Let K be a complete ultrametric algebraically closed ﬁeld. Given r > 0, we deﬁne the disks d(0, r) and d(0, r − ) by d(0, r) = {x ∈ K / |x| ≤ r} and d(0, r − ) = {x ∈ K / |x| < r}.

### 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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