p-adic Functional Analysis

N. De Grande-De Kimpe, Jerzy Kakol, C. Perez-Garcia

• 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.

". . .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."---Mathematica Bohemica