Asymptotic phase, asymptotic modulus, and Titchmarsh-Weyl coefficient for a Dirac system

DOI10.1016/0022-247X(89)90169-8zbMath0738.34044OpenAlexW2095580630MaRDI QIDQ1812685

Martin Klaus, J. K. Shaw, Don B. Hinton

Publication date: 25 June 1992

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(89)90169-8

zbMATH Keywords

spectral functionseries representationJost functionasymptotic phaseDirac systemasymptotic form of the Titchmarsh-Weyl coefficientscattering formulas

Mathematics Subject Classification ID

Particular ordinary differential operators (Dirac, one-dimensional Schrödinger, etc.) (34L40) Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. (34A25) Weyl theory and its generalizations for ordinary differential equations (34B20) Scattering theory, inverse scattering involving ordinary differential operators (34L25)

Related Items (max. 100)

On the classes of explicit solutions of Dirac, dynamical Dirac and Dirac-Weyl systems with non-vanishing at infinity potentials, their properties and applications ⋮ Weyl–Titchmarsh $M$-Function Asymptotics, Local Uniqueness Results, Trace Formulas, and Borg-type Theorems for Dirac Operators ⋮ Resonances for the radial Dirac operators ⋮ Resonances for Dirac operators on the half-line ⋮ The form of the spectral functions associated with Dirac equations

Cites Work

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• ABSOLUTELY CONTINUOUS SPECTRA OF DIRAC SYSTEMS WITH LONG RANGE, SHORT RANGE AND OSCILLATING POTENTIALS
• The Asymptotic Form of the Titchmarsh-Weyl m -Function Associated with a Dirac System
• An exact method for the calculation of certain Titchmarsh-Weyl m-functions
• Levinson's theorem and Titchmarsh-Weyl m(λ) theory for Dirac systems*
• The virial theorem and its application to the spectral theory of Schrödinger operators
• AN EXAMPLE IN THE THEORY OF THE SPECTRUM OF A FUNCTION

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