Spectral properties of the complex Airy operator on the half-line

DOI10.1007/s10688-017-0168-1zbMath1372.34131OpenAlexW2596609709MaRDI QIDQ2364482

A. A. Shkalikov, Artem M. Savchuk

Publication date: 21 July 2017

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10688-017-0168-1

zbMATH Keywords

Schrödinger operatornonself-adjoint operatorcompleteness of the eigenfunctions of a differential operatorcomplex Airy operator

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Eigenfunctions, eigenfunction expansions, completeness of eigenfunctions of ordinary differential operators (34L10) Boundary value problems on infinite intervals for ordinary differential equations (34B40) Eigenvalues, estimation of eigenvalues, upper and lower bounds of ordinary differential operators (34L15)

Related Items (16)

Completeness theorem for the system of eigenfunctions of the complex Schrödinger operator \(\mathscr{L}_{c , \alpha} = - d^2 / d x^2 + c x^\alpha \) ⋮ On analytic perturbations of a non-self-adjoint anharmonic oscillator ⋮ Spectral properties of the nonsectorial Sturm-Liouville operator on the semiaxis ⋮ Inverse spectral problem for the Schrödinger equation with an additional linear potential ⋮ On the transformation operator for the Schrödinger equation with an additional linear potential ⋮ SCATTERING PROBLEM OF THE PERTURBED AIRY EQUATION ON A HALF-AXIS ⋮ Inverse spectral problem for the one-dimensional Stark operator on the semiaxis ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Completeness theorem for the system of eigenfunctions of the complex Schrödinger operator \(\mathcal{L}_c = - d^2 / d x^2 + c x^{2 / 3} \) ⋮ Unnamed Item ⋮ A note on the Schrodinger operator with exponential potential ⋮ Conditions of spectrum localization for operators not close to self-adjoint operators ⋮ Inverse scattering problem for the Schrödinger equation with an additional quadratic potential on the entire axis ⋮ A completeness theorem for the system of eigenfunctions of the complex Schrödinger operator with potential \(q(x)=cx^\alpha \) ⋮ The finiteness of the spectrum of boundary value problems defined on a geometric graph

Uses Software

• Eigtool

Cites Work

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• Spectral instability for even non-selfadjoint anharmonic oscillators
• Eigensystem of an \(L ^{2}\)-perturbed harmonic oscillator is an unconditional basis
• Spectral projections of the complex cubic oscillator
• Differential operators admitting various rates of spectral projection growth
• Spectral portraits of the Orr-Sommerfeld operator with large Reynolds numbers
• On the basis property of root vectors of a perturbed self-adjoint operator
• The spectrum of a harmonic oscillator operator perturbed by point interactions
• High energy eigenfunctions of one-dimensional Schrödinger operators with polynomial potentials
• The limit behavior of the spectrum for large parameter values in a model problem
• Semi-classical states for non-self-adjoint Schrödinger operators
• Pseudospectra of the Schrödinger operator with a discontinuous complex potential
• On the spectrum localization of the Orr--Sommerfeld problem for large Reynolds numbers
• On a model problem for the Orr-Sommerfeld equation with linear profile
• Spectral instability of some non-selfadjoint anharmonic oscillators
• Local form-subordination condition and Riesz basisness of root systems
• Root system of singular perturbations of the harmonic oscillator type operators
• Perturbations of self-adjoint and normal operators with discrete spectrum
• Pseudospectra in non-Hermitian quantum mechanics
• The Stability of the Normal State of Superconductors in the Presence of Electric Currents
• Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
• Wild Spectral Behaviour of Anharmonic Oscillators
• SPECTRAL ASYMPTOTICS OF THE NON-SELF-ADJOINT HARMONIC OSCILLATOR
• On the limit behaviour of the spectrum of a model problem for the Orr-Sommerfeld equation with Poiseuille profile
• Riesz bases consisting of root functions of 1D Dirac operators
• The Complex Airy Operator on the Line with a Semipermeable Barrier

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