By Jesus Araujo-gomez, Bertin Diarra, Alain Escassut
This quantity comprises papers according to 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 the following characteristic contemporary advancements in a number of components of non-Archimedean research: Hilbert and Banach areas, finite dimensional areas, topological vector areas and operator idea, strict topologies, areas of constant services and of strictly differentiable capabilities, isomorphisms among Banach services areas, and degree and integration. different subject matters mentioned during this quantity contain $p$-adic differential and $q$-difference equations, rational and non-Archimedean analytic services, the spectrum of a few algebras of analytic features, and maximal beliefs of the ultrametric corona algebra
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Additional info for Advances in non-Archimedean Analysis: 11th International Conference P-adic Functional Analysis July 5-9, 2010 Universite Blaise Pascal, Clermont-ferrand, France
Navarro. In  they characterized the nuclearity of the space C(X, E) of continuous functions from X to E, equipped with the compact open topology. First they considered the case when E = K (it is a customary to write C(X) instead of C(X, K)). Then the case of vector-valued continuous functions was solved, as a combination of the K-valued case and some results that they proved there about preservation of nuclearity under topological tensor products. Finally they arrived in  at the next characterization of nuclearity.
Sci. Math. 45 (1997), 313-321.  (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.  (with S. Albeverio, R. Y. Khrennikov) p-Adic probability and an interpretation of negative probabilities in quantum mechanics.
And the following conditions hold simultaneously: (1) b0 ≡ 1 (mod 2), b0 + b1 ≡ 3 (mod 4), b2 + b3 ≡ 2 (mod 4); (2) |bm |2 = 1 for m ≥ 2; 2n −1 (3) m=2n−1 bm ≡ 0 (mod 4) for n ≥ 3. 3 is the following lemma whose proof, in turn, uses results announced in  by the third of authors of the present paper. 4. 1). t. the measure μp ) if and only if the following conditions hold simultaneously: (1) B0 ≡ 1 (mod 2), B0 + B1 ≡ 3 (mod 4), (2) |Bm |2 = 2− log2 m , if m ≥ 2; (3) 2n −1 m=2n−1 (Bm − 2n−1 ) 2 ≤ 2−(n+1) , if n ≥ 2.
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