A discrete fixed point theorem of Eilenberg as a particular case of the contraction principle.
Analytic functions over valued fields.
Banach Spaces Over Topological Semifields and Common Fixed Points
-semigroups of linear operators on some ultrametric Banach spaces.
Calcul pseudodifférentiel -adique
Corrigendum to “Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space”
Erratum to: “Towards a theory of some unbounded linear operators on -adic Hilbert spaces and applications”
Functional calculus for a class of unbounded linear operators on some non-archimedean Banach spaces
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 . For that, our first task consists of introducing a new class of linear operators denoted 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.
Logarithmic and antilogarithmic mappings [Book]
Non-Archimedean valued quasi-invariant descending at infinity measures.
On a general type of -adic parabolic equations.
On non-archimedean locally convex spaces
p-adic Ascoli theorems.
The aim of this paper is the study of a certain class of compact-like sets within some spaces of continuous functions over non-Archimedean ground fields. As a result, some p-adic Ascoli theorems are obtained.
Representation of bilinear forms in non-Archimedean Hilbert space by linear operators
The paper considers representing symmetric, non-degenerate, bilinear forms on some non-Archimedean Hilbert spaces by linear operators. Namely, upon making some assumptions it will be shown that if is a symmetric, non-degenerate bilinear form on a non-Archimedean Hilbert space, then is representable by a unique self-adjoint (possibly unbounded) operator .
Representation of bilinear forms in non-Archimedean Hilbert space by linear operators II
The paper considers the representation of non-degenerate bilinear forms on the non-Archimedean Hilbert space by linear operators. More precisely, upon making some suitable assumptions we prove that if is a non-degenerate bilinear form on , then is representable by a unique linear operator whose adjoint operator exists.
Some more Steinhaus type theorems over valued fields
Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space
The paper is concerned with the spectral analysis for the class of linear operators in non-archimedean Hilbert space, where is a diagonal operator and is a rank one operator. The results of this paper turn out to be a generalization of those results obtained by Diarra.
Spectral integration and spectral theory for non-Archimedean Banach spaces.
Tauberian operators in -adic analysis.
The use of operators for the construction of normal bases for the space of continuous functions on .