Differential operators admitting various rates of spectral projection growth

Abstract

We consider families of non-self-adjoint perturbations of self-adjoint harmonic and anharmonic oscillators. The norms of spectral projections of these operators are found to grow at intermediate rates from arbitrarily slowly to exponentially rapidly.

35 pages, significant revisions, accepted version (published version may differ)

References in corpus (3)

• Root system of singular perturbations of the harmonic oscillator type operators
• The spectrum of a Harmonic Oscillator Operator Perturbed by Point Interactions
• Eigenvalue Asymptotics of Perturbed Self-adjoint Operators

Cited by in corpus (12)

• Pseudospectra in non-Hermitian quantum mechanics
• Root system of singular perturbations of the harmonic oscillator type operators
• Local form-subordination condition and Riesz basisness of root systems
• Generalized Riesz systems and orthonormal sequences in Krein spaces
• Pseudospectra of the Schroedinger operator with a discontinuous complex potential
• A Bound on the Pseudospectrum of the Harmonic Oscillator with Imaginary Cubic Potential
• Bifurcation of nonlinear eigenvalues in problems with antilinear symmetry
• Concentration of eigenfunctions of Schroedinger operators
• The shifted harmonic oscillator and the hypoelliptic Laplacian on the circle
• On dual definite subspaces in Krein space
• The pseudospectrum of an operator with Bessel-type singularities
• Spectral properties of complex Airy operator on the semi-axis