On the second quantisation of Hilbert-Schmidt processes
On the shift operators.
On the singular continuous spectrum of self-adjoint extensions.
On the singular numbers for some integral operators.
Two-sided estimates of Schatten-von Neumann norms for weighted Volterra integral operators are established. Analogous problems for some potential-type operators defined on Rn are solved.
On the singular values and eigenvalues of the Fox-Li and related operators.
On the solution of homogeneous functional equations in Hilbert space
On the solvability of the Lyapunov equation for nonselfadjoint differential operators of order 2m with nonlocal boundary conditions
This paper is devoted to the solvability of the Lyapunov equation A*U + UA = I, where A is a given nonselfadjoint differential operator of order 2m with nonlocal boundary conditions, A* is its adjoint, I is the identity operator and U is the selfadjoint operator to be found. We assume that the spectra of A* and -A are disjoint. Under this restriction we prove the existence and uniqueness of the solution of the Lyapunov equation in the class of bounded operators.
On the space of φ-nuclear operators on l2.
We consider the generalization Sphi of the Schatten classes Sp obtained in correspondence with opportune continuous, strictly increasing, sub-additive functions phi such that phi(0) = 0 and phi(1) = 1. The purpose of this note is to study the spaces Sphi of the phi-nuclear operators and to compare their properties to those of the by now well-known space S1 of nuclear operators.
On the Spectra of Finite-Dimensional Pertobations of Matrix Multiplication Operators.
On the spectra of some non-normal operators.
On the spectral function of a normal operator
On the Spectral Kernel of Symmetric Extensions.
On the spectral multiplicity of a direct sum of operators
We calculate the spectral multiplicity of the direct sum T⊕ A of a weighted shift operator T on a Banach space Y which is continuously embedded in and a suitable bounded linear operator A on a Banach space X.
On the spectral radius of positive operators.
On the spectral radius of positive operators (Corrigendum).
On the spectrum of orthomorphisms and Barbashin operators.
On the spectrum of Robin Laplacian in a planar waveguide
We consider the Laplace operator in a planar waveguide, i.e. an infinite two-dimensional straight strip of constant width, with Robin boundary conditions. We study the essential spectrum of the corresponding Laplacian when the boundary coupling function has a limit at infinity. Furthermore, we derive sufficient conditions for the existence of discrete spectrum.
On the spectrum of singularly perturbed operators
On the spectrum of the operator which is a composition of integration and substitution
Let ϕ: [0,1] → [0,1] be a nondecreasing continuous function such that ϕ(x) > x for all x ∈ (0,1). Let the operator be defined on L₂[0,1]. We prove that has a finite number of nonzero eigenvalues if and only if ϕ(0) > 0 and ϕ(1-ε) = 1 for some 0 < ε < 1. Also, we show that the spectral trace of the operator always equals 1.
On the Spherical Spectrum.