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This paper is mainly concerned with extensions of the so-called Vishik functional calculus for analytic bounded linear operators to a class of unbounded linear operators on $c_{0}$ . For that, our first task consists of introducing a new class of linear operators denoted $W (c_{0} (J, ω, 𝕂))$ and next we make extensive use of such a new class along with the concept of convergence in the sense of resolvents to construct a functional calculus for a large class of unbounded linear operators.

Generalized Hyers-Ulam stability of an AQCQ-functional equation in non-Archimedean Banach spaces.

Park, Choonkil, Gordji, Madjid Eshaghi, Najati, Abbas (2010)

The Journal of Nonlinear Sciences and its Applications

Harmonic analysis on $p$ -torsional groups

Marius Van der Put (1978/1979)

Groupe de travail d'analyse ultramétrique

Hyers-Ulam-Rassias stability of the Apollonius type quadratic mapping in RN-spaces.

Kenary, H.Azadi, Shafaat, Kh., Shafei, M., Takbiri, G. (2011)

The Journal of Nonlinear Sciences and its Applications

Idéaux de fonctions analytiques bornées stables par dérivation

Jean-Paul Bezivin (1976/1977)

Groupe de travail d'analyse ultramétrique

Indice d’un opérateur différentiel $p$ -adique IV. Cas des systèmes. Mesure de l’irrégularité dans un disque

Philippe Robba (1985)

Annales de l'institut Fourier

Nous désirons savoir si l’opérateur différentiel d’ordre $1, \frac{d}{d x} + G$ , où $G$ est une $k \times k$ matrice à coefficients rationnels, a un indice dans l’espace des fonctions analytiques dans une boule; dans le cas où cet indice existe nous voulons aussi le calculer. Dans le cas où $k = 1$ nous montrons l’existence d’un indice (si l’exposant de l’opérateur n’est pas Liouville $p$ -adique) et nous montrons comment calculer cet indice. De même nous savons montrer l’existence d’un indice et comment calculer cet indice lorsque le système...

Indiscernibles and dimensional compactness

C. Ward Henson, Pavol Zlatoš (1996)

Commentationes Mathematicae Universitatis Carolinae

This is a contribution to the theory of topological vector spaces within the framework of the alternative set theory. Using indiscernibles we will show that every infinite set $u S \subseteq G$ in a biequivalence vector space $〈 W, M, G 〉$ , such that $x - y \notin M$ for distinct $x, y \in u$ , contains an infinite independent subset. Consequently, a class $X \subseteq G$ is dimensionally compact iff the $π$ -equivalence $≐_{M}$ is compact on $X$ . This solves a problem from the paper [NPZ 1992] by J. Náter, P. Pulmann and the second author.

Integrable functions for the Bernoulli measures of rank $1$

Hamadoun Maïga (2010)

Annales mathématiques Blaise Pascal

In this paper, following the $p$ -adic integration theory worked out by A. F. Monna and T. A. Springer [4, 5] and generalized by A. C. M. van Rooij and W. H. Schikhof [6, 7] for the spaces which are not $σ$ -compacts, we study the class of integrable $p$ -adic functions with respect to Bernoulli measures of rank $1$ . Among these measures, we characterize those which are invertible and we give their inverse in the form of series.

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