Algebraic sum of unbounded normal operators and the square root problem of Kato
Towards a theory of some unbounded linear operators on -adic Hilbert spaces and applications
We are concerned with some unbounded linear operators on the so-called -adic Hilbert space . Both the Closedness and the self-adjointness of those unbounded linear operators are investigated. As applications, we shall consider the diagonal operator on , and the solvability of the equation where is a linear operator on .
Erratum to: “Towards a theory of some unbounded linear operators on -adic Hilbert spaces and applications”
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 .
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.
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.
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.
Corrigendum to “Spectral analysis for rank one perturbations of diagonal operators in non-archimedean Hilbert space”
Fractional powers of hyponormal operators of Putnam type.
Existence of pseudo-almost automorphic mild solutions to some nonautonomous partial evolution equations.
Existence of doubly-weighted pseudo almost periodic solutions to non-autonomous differential equations.
Pseudo almost periodic solutions to some differential equations with infinite delay.
Existence of pseudo almost periodic solutions to some classes of partial hyperbolic evolution equations.
-semigroups of linear operators on some ultrametric Banach spaces.
Schrödinger operators with a singular potential.
A generalization related to Schrödinger operatorswith a singular potential.
An application to Kato's square root problem.
Existence of almost automorphic solutions to some neutral functional differential equations with infinite delay.
Existence of pseudo almost automorphic solutions for the heat equation with -pseudo almost automorphic coefficients.
Existence of quadratic-mean almost periodic solutions to some stochastic hyperbolic differential equations.
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