Odd anharmonic oscillators and shape resonances
On a formula for the jumps in the semi-Fredholm domain.
In this paper we prove some properties of the lower s-numbers and derive asymptotic formulae for the jumps in the semi-Fredholm domain of a bounded linear operator on a Banach space.
On a Weyl-von Neumann type theorem for antilinear self-adjoint operators
Antilinear operators on a complex Hilbert space arise in various contexts in mathematical physics. In this paper, an analogue of the Weyl-von Neumann theorem for antilinear self-adjoint operators is proved, i.e. that an antilinear self-adjoint operator is the sum of a diagonalizable operator and of a compact operator with arbitrarily small Schatten p-norm. On the way, we discuss conjugations and their properties. A spectral integral representation for antilinear self-adjoint operators is constructed....
On an estimate for the norm of a function of a quasihermitian operator
Let A be a closed linear operator acting in a separable Hilbert space. Denote by co(A) the closed convex hull of the spectrum of A. An estimate for the norm of f(A) is obtained under the following conditions: f is a holomorphic function in a neighbourhood of co(A), and for some integer p the operator is Hilbert-Schmidt. The estimate improves one by I. Gelfand and G. Shilov.
On Cusp Forms in Character Varieties.
On estimates for spectral projections of perturbed selfadjoint operators.
On generalized a-Browder's theorem
We characterize the bounded linear operators T satisfying generalized a-Browder's theorem, or generalized a-Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H₀(λI - T) as λ belongs to certain sets of ℂ. In the last part we give a general framework in which generalized a-Weyl's theorem follows for several classes of operators.
On generalized property (v) for bounded linear operators
An operator T acting on a Banach space X has property (gw) if , where is the approximate point spectrum of T, is the upper semi-B-Weyl spectrum of T and E(T) is the set of all isolated eigenvalues of T. We introduce and study two new spectral properties (v) and (gv) in connection with Weyl type theorems. Among other results, we show that T satisfies (gv) if and only if T satisfies (gw) and .
On -quasi-derivatives for solutions of perturbed general quasi-differential equations
This paper is concerned with square integrable quasi-derivatives for any solution of a general quasi-differential equation of th order with complex coefficients , provided that all th quasi-derivatives of solutions of and all solutions of its normal adjoint are in and under suitable conditions on the function .
On perturbations of deviations of periodic differential-difference equations in Banach spaces
On Perturbations of Linear m-Accetive Operators on Reflexive Banach Spaces.
On polynomial equations in Banach space, perturbation techniques and applications.
On random evolutions induced by countable state space Markov chains
On stability of classes of Lipschitz mappings generated by compact sets of linear mappings.
On the dependence of the orthogonal projector on deformations of the scalar product
We consider scalar products on a given Hilbert space parametrized by bounded positive and invertible operators defined on this space, and orthogonal projectors onto a fixed closed subspace of the initial Hilbert space corresponding to these scalar products. We show that the projector is an analytic function of the scalar product, we give the explicit formula for its Taylor expansion, and we prove some algebraic formulas for projectors.
On the domain of selfadjoint extension of the product of Sturm-Liouville differential operators.
On the existence of solution of the equation and a generalized coincidence degree theory. I.
On the existence of solution of the equation and a generalized coincidence degree theory. II.
On the Perturbation Theory for Strongly Continuous Semigroups.
On the Relative Completeness of the Generalized Eigenvectors of Elliptic Eigenvalue Problems with Indefinite Weight Functions.