35 citations · 72 across the 13 of their papers we have counts for
16 papers
The abstract Birman-Schwinger principle and spectral stability
Marcel Hansmann, David Krejcirik
We discuss abstract Birman-Schwinger principles to study spectra of self-adjoint operators subject to small non-self-adjoint perturbations in a factorised form. In particular, we e…
Bounds on the first Betti number - an approach via Schatten norm estimates on semigroup differences
Marcel Hansmann, Christian Rose, Peter Stollmann
We derive new estimates for the first Betti number of compact Riemannian manifolds. Our approach relies on the Birman-Schwinger principle and Schatten norm estimates for semigroup…
Eigenvalues of compactly perturbed operators via entropy numbers
Marcel Hansmann
We derive new estimates for the number of discrete eigenvalues of compactly perturbed operators on Banach spaces, assuming that the perturbing operator is an element of a weak entr…
Some remarks on upper bounds for Weierstrass primary factors and their application in spectral theory
Marcel Hansmann
We study upper bounds on Weierstrass primary factors and discuss their application in spectral theory. One of the main aims of this note is to draw attention to works of Blumenthal…
Perturbation determinants in Banach spaces - with an application to eigenvalue estimates for perturbed operators
Marcel Hansmann
In the first part of this paper we provide a self-contained introduction to (regularized) perturbation determinants for operators in Banach spaces. In the second part, we use these…
Estimating the number of eigenvalues of linear operators on Banach spaces
Michael Demuth, Franz Hanauska, Marcel Hansmann +1
Let be a bounded operator on a Banach space, and consider a perturbation , where is compact. This work is concerned with obtaining bounds on the number of eigenv…
An observation concerning boundary points of the numerical range
Marcel Hansmann
A theorem of Hübner states that non-round boundary points of the numerical range of a linear operator, i.e. points where the boundary has infinite curvature, are contained in the s…
On non-round points of the boundary of the numerical range and an application to non-selfadjoint Schrödinger operators
Marcel Hansmann
We show that non-round boundary points of the numerical range of an unbounded operator (i.e. points where the boundary has infinite curvature) are contained in the spectrum of the…
Eigenvalues of non-selfadjoint operators: A comparison of two approaches
Michael Demuth, Marcel Hansmann, Guy Katriel
The central problem we consider is the distribution of eigenvalues of closed linear operators which are not selfadjoint, with a focus on those operators which are obtained as pertu…
Variation of discrete spectra for non-selfadjoint perturbations of selfadjoint operators
Marcel Hansmann
Let B=A+K where A is a bounded selfadjoint operator and K is an element of the von Neumann-Schatten ideal S_p with p>1. Let {λ_n} denote an enumeration of the discrete spectrum of…
Absence of eigenvalues of non-selfadjoint Schrödinger operators on the boundary of their numerical range
Marcel Hansmann
We use a classical result of Hildebrandt to establish simple conditions for the absence of eigenvalues of non-selfadjoint discrete and continuous Schrödinger operators on the bound…
From spectral theory to bounds on zeros of holomorphic functions
Marcel Hansmann, Guy Katriel
We show how eigenvalue estimates for linear operators can be used to obtain new Blaschke type bounds on zeros of holomorphic functions on the unit disk.
An eigenvalue estimate and its application to non-selfadjoint Jacobi and Schrödinger operators
Marcel Hansmann
For bounded linear operators on a Hilbert space we show the validity of the estimate $$ \sum_{λ\in σ_d (B)} \dist(λ, \overline{\num}(A))^p \leq \| B-A \|_{\math…
On the discrete spectrum of non-selfadjoint operators
Michael Demuth, Marcel Hansmann, Guy Katriel
We prove quantitative bounds on the eigenvalues of non-selfadjoint unbounded operators obtained from selfadjoint operators by a perturbation that is relatively-Schatten. These boun…
Inequalities for the eigenvalues of non-selfadjoint Jacobi operators
Marcel Hansmann, Guy Katriel
We prove Lieb-Thirring-type bounds on eigenvalues of non-selfadjoint Jacobi operators, which are nearly as strong as those proven previously for the case of selfadjoint operators b…
On the distribution of eigenvalues of non-selfadjoint operators
Michael Demuth, Marcel Hansmann, Guy Katriel
We prove quantitative bounds on the eigenvalues of non-selfadjoint bounded and unbounded operators. We use the perturbation determinant to reduce the problem to one of studying the…