Differential Operators with Perturbed Domains

On the point spectrum of some perturbed differential operators with periodic coefficients

Finiteness of the point spectrum of linear operators acting in a Banach space is investigated from point of view of perturbation theory. In the first part of the paper we present an abstract result based on analytical continuation of the resolvent function through continuous spectrum. In the second part, the abstract result is applied to differential operators which can be represented as a diff...

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

Determinant Type Differential Operators on Homogeneous Siegel Domains

In harmonic analysis on classical domains of matrices, the differential operator whose symbol is the determinant polynomial plays important roles. Particularly, the operator is substantial in study of invariant Hilbert spaces of holomorphic functions on the domain [1, 2, 7, 14, 15, 21]. Considering the Siegel domain realization of a certain symmetric domain with Fourier-analytic methods, Jakobs...

Lipschitz Functions of Perturbed Operators

We prove that if f is a Lipschitz function on R, A and B are self-adjoint operators such that rank(A − B) = 1, then f(A) − f(B) belongs to the weak space S1,∞, i.e., sj(A − B) ≤ const(1 + j). We deduce from this result that if A − B belongs to the trace class S1 and f is Lipschitz, then f(A) − f(B) ∈ SΩ, i.e., Pn j=0 sj(f(A) − f(B)) ≤ const log(2 + n). We also obtain more general results about ...

Joint Analyticity and Analytic Continuation of Dirichlet– Neumann Operators on Doubly Perturbed Domains

Abstract. In this paper we take up the question of analyticity properties of Dirichlet–Neumann operators (DNO) which arise in boundary value and free boundary problems from a wide variety of applications (e.g., fluid and solid mechanics, electromagnetic and acoustic scattering). More specifically, we consider DNO defined on domains inspired by the simulation of ocean waves over bathymetry, i.e....