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Weyl’s Laws and Connes’ Integration Formulas for Matrix-Valued \(L\!\log \!L\)-Orlicz Potentials
Thanks to the Birman-Schwinger principle, Weyl’s laws for Birman-Schwinger operators yields semiclassical Weyl’s laws for the corresponding...
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Quantitative Bounds Versus Existence of Weakly Coupled Bound States for Schrödinger Type Operators
It is well-known that for usual Schrödinger operators weakly coupled bound states exist in dimensions one and two, whereas in higher dimensions the...
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Schrödinger Operators with Complex Sparse Potentials
We establish quantitative upper and lower bounds for Schrödinger operators with complex potentials that satisfy some weak form of sparsity. Our first...
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A noncommutative Tauberian theorem and Weyl asymptotics in noncommutative geometry
We prove a Tauberian theorem for singular values of noncommuting operators which allows us to prove exact asymptotic formulas in noncommutative...
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Weak coupling limit for Schrödinger-type operators with degenerate kinetic energy for a large class of potentials
We improve results by Frank, Hainzl, Naboko, and Seiringer (J Geom Anal 17(4):559–567, 2007) and Hainzl and Seiringer (Math Nachr 283(3):489–499,...
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Eigenvalues of the Linearized 2D Euler Equations via Birman–Schwinger and Lin’s Operators
We study spectral instability of steady states to the linearized 2D Euler equations on the torus written in vorticity form via certain...
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The two lowest eigenvalues of the harmonic oscillator in the presence of a Gaussian perturbation
In this note, we consider a one-dimensional quantum mechanical particle constrained by a parabolic well perturbed by a Gaussian potential. As the...
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Heat kernels of the discrete Laguerre operators
For the discrete Laguerre operators we compute explicitly the corresponding heat kernels by expressing them with the help of Jacobi polynomials. This...
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On a Conjecture by Hundertmark and Simon
The main result of this paper is a complete proof of a new Lieb–Thirring-type inequality for Jacobi matrices originally conjectured by Hundertmark...
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On the Existence of Linearly Oscillating Galaxies
We consider two classes of steady states of the three-dimensional, gravitational Vlasov-Poisson system: the spherically symmetric Antonov-stable...
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Dirac Operators with a δ-Shell Interaction
AbstractSummarizing a talk given at the Bogolyubov 2019 conference, we review recent results concerning Dirac operators with a singular interaction...
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Union of Discretized Spectra for Scattering Calculations
AbstractHere we propose a new technique which allows to find scattering phase shifts and parameters of resonances directly from the discretized...
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On the Point Spectrum in the Ekman Boundary Layer Problem
New eigenvalue enclosures for the block operator problem arising in the study of stability of the Ekman boundary layer are proved. This solves an...
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Functional-Difference Equations and Their Link with Perturbations of the Mehler Operator
AbstractThis work deals with the spectral properties of the functional-difference equations that arise in a number of applications in the...
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Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal \(\delta '\) interactions
The objective of the present paper is the study of a one-dimensional Hamiltonian with the interaction term given by the sum of two nonlocal...
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Schrödinger operator in a half-plane with the Neumann condition on the boundary and a singular \(\delta\)-potential supported by two half-lines, and systems of functional-difference equations
AbstractWe study the asymptotics with respect to distance for the eigenfunction of the Schrödinger operator in a half-plane with a singular
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