A presentation of results in p-adic Banach spaces, spaces over fields with an infinite rank valuation, Frechet (and locally convex) spaces with Schauder bases, function spaces, p-adic harmonic analysis, and related areas. It showcases research results in functional analysis over nonarchimedean valued complete fields. It explores spaces of continuous functions, isometries, Banach Hopf algebras, summability methods, fractional differentiation over local fields, and adelic formulas for gamma- and beta-functions in algebraic number theory.
". . .contains many new results and up-to-date information about current developments in the field. . .of interest to anyone actively working in p-acidic analysis."
Strict topologies and duals in spaces of functions; ultrametric weakly separating maps with closed range; analytic spectrum of an algebra of strictly analytic p-adic functions; an improvement of the p-adic Nevanlinna theory and application to meromorphic functions; an application of C-compactness; on the integrity of the dual algebra of some complete ultrametric Hopf algebras; on p-adic power series; Hartogs-Stawski's theorem in discrete valued fields; the Fourier transform for p-adic tempered distributions; on the Mahler coefficients of the logarithmic derivative of the p-adic gamma function; p-adic (dF) spaces; on the weak basis theorems for p-adic locally convex spaces; fractional differentiation operator over an infinite extension of a local field; some remarks on duality of locally convex BK-modules; spectral properties of p-adic Banach algebras; surjective isometries of space of continuous functions; on the algebras (c,c) and (l-alpha, l-alpha) in nonarchimedean fields; Banach spaces over fields with an infinite rank valuation; the p-adic Banach-Dieudonne Theorem and semicompact inductive limits; Mahler's and other bases for p-adic continuous functions; orthonormal bases for nonarchimedean Banach spaces of continuous functions.