Vladimir Georgescu

On the point spectrum of Dirac operators

Abstract We study the decay of eigenfunctions and we give conditions for the absence of eigenvalues embedded in the continuous spectrum for Dirac Hamiltonians with long range and locally singular potential.

Riesz–Kolmogorov Compactness Criterion, Lorentz Convergence and Ruelle Theorem on Locally Compact Abelian Groups

Ruelles theorem gives, for a certain class of self-adjoint operators on L2(Rn), a description of the pure point and continuous spectral subspaces of the operator in terms of bound and scattering states. We extend this characterization to arbitrary self-adjoint operators acting in L2(X), where X is an Abelian locally compact group. We replace the convergence in Cesàro mean from the standard version of Ruelles theorem by convergence in Lorentz sense, which is sharper than any convergence in invariant mean sense. Our main tool is a description in term of position and momentum observables of relatively compact subsets of L2(X) extending the Riesz–Kolmogorov theorem.

Resolvent and propagation estimates for Klein-Gordon equations with non-positive energy

We study in this paper an abstract class of Klein-Gordon equations: \[ \p_{t}^{2}\phi(t)- 2\i k \p_{t}\phi(t)+ h \phi(t)=0, \] where

Spectral Analysis of Quantum Field Models with a Particle Number Cutoff

\phi: \rr\to \cH

On the Virial Theorem in Quantum Mechanics

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Crossed products of C*-algebras and spectral analysis of quantum hamiltonians

\cH

Commutators, C0-semigroups and resolvent estimates

is a (complex) Hilbert space, and

Spectral Theory of Massless Pauli-Fierz Models

h

Isometries, Fock spaces, and spectral analysis of Schrödinger operators on trees

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Homogeneous Schrödinger Operators on Half-Line

k