Complex Powers of Nondensely Defined Operators

Existence Results for Semilinear Perturbed Functional Differential Equations with Nondensely Defined Operators

Integral Solutions of Fractional Evolution Equations with Nondense Domain

In this article, we study the existence of integral solutions for two classes of fractional order evolution equations with nondensely defined linear operators. First, we consider the nonhomogeneous fractional order evolution equation and obtain its integral solution by Laplace transform and probability density function. Subsequently, based on the form of integral solution for nonhomogeneous fra...

Note on multiplicative perturbation of local C-regularized cosine functions with nondensely defined generators

In this note, we obtain a new multiplicative perturbation theorem for local Cregularized cosine function with a nondensely defined generator A. An application to an integrodifferential equation is given.

Finite Rank Perturbations, Scattering Matrices and Inverse Problems

In this paper the scattering matrix of a scattering system consisting of two selfadjoint operators with finite dimensional resolvent difference is expressed in terms of a matrix Nevanlinna function. The problem is embedded into an extension theoretic framework and the theory of boundary triplets and associated Weyl functions for (in general nondensely defined) symmetric operators is applied. Th...

Operator Holes and Extensions of Sectorial Operators and Dual Pairs of Contractions

A description of the set of m-sectorial extensions of a dual pair {A1, A2} of nonnegative operators is obtained. Some classes of nonaccretive extensions of the dual pair {A1, A2} are described too. Both problems are reduced to similar problems for a dual pair {T1, T2} of nondensely defined symmetric contractions Tj = (I−Aj)(I+Aj), j ∈ {1, 2}. In turn these problems are reduced to the investigat...