Spectral theory?50 years of progress and a conclusion

DOI10.1002/MMA.211zbMath0991.47033OpenAlexW2015514137MaRDI QIDQ2725065

D. B. Pearson

Publication date: 12 July 2001

Published in: Mathematical Methods in the Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/mma.211

zbMATH Keywords

spectral measurespectral analysislimit pointlimit circleWeyl theorysecond-order linear ordinary differential operatorsWeyl-Titshmarsh \(m\)-function

Mathematics Subject Classification ID

Weyl theory and its generalizations for ordinary differential equations (34B20) General spectral theory of ordinary differential operators (34L05) General theory of ordinary differential operators (47E05) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10)

Cites Work

• On subordinacy and analysis of the spectrum of one-dimensional Schrödinger operators
• Singular continuous measures in scattering theory
• The absolute continuous spectrum of one-dimensional Schrödinger operators with decaying potentials
• Welsh eigenvalues of radially periodic Schrödinger operators
• On the absolutely continuous spectrum of one-dimensional Schrödinger operators with square summable potentials
• Absolutely continuous spectra of one-dimensional Schrödinger operators and Jacobi matrices with slowly decreasing potentials
• Stability of the absolutely continuous spectrum of the Schrödinger equation under slowly decaying perturbations and a. e. convergence of integral operators
• Schrödinger operators in the twentieth century
• Spectral Theory for Slowly Oscillating Potentials II. Schrödinger Operators
• On subordinacy and analysis of the spectrum of Schrödinger operators with two singular endpoints
• On subordinacy and spectral multiplicity for a class of singular differential operators
• Absolutely continuous spectrum for one-dimensional Schrödinger operators with slowly decaying potentials: Some optimal results
• Operators with singular continuous spectrum, V. Sparse potentials

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