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• W2021770942 abstract "Communications on Pure and Applied MathematicsVolume 12, Issue 3 p. 523-542 Article On the discreteness of spectra of singular Sturm-Liouville problems Jerome Berkowitz, Jerome BerkowitzSearch for more papers by this author Jerome Berkowitz, Jerome BerkowitzSearch for more papers by this author First published: August 1959 https://doi.org/10.1002/cpa.3160120309Citations: 18AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Bibliography 1 Weyl, H., Über gewöhnliche lineare Differentialgleichungen mit singulären Stellen und ihre Eigenfunktionen, Nachr. Akad. Wiss. Göttingen. Math.-Phys. Kl. Math.-Phys.-Chem. Abt., 1909, pp. 37–63; Über gewöhnliche lineare Differentialgleichungen mit singulären Stellen und ihre Eigenfunktionen 1910, pp. 442–467. 2 Weyl, H., Über beschränkte quadratische Formen, deren Differenz vollstetig ist, Rend. Circ. Mat. Palermo, Vol. 27, 1909, pp. 373–392. 3 Weyl, H., Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen, Math. Ann., Vol. 68, 1910, pp. 220–269. 4 Courant, R., and Hilbert, D., Methods of Mathematical Physics, Vol. 1, Interscience Publishers, 1953, especially Chapter VI, pp. 451–455, 463–464. 5 Prüfer, H., Neue Herleitung der Sturm-Liouvilleschen Reihentwicklung stetiger Funktionen, Math. Ann., Vol. 96, 1926, pp. 499–518. 6 Stone, M. H., Linear transformations in Hilbert space and their applications to analysis, Amer. Math. Soc., New York, 1932, pp. 448–530. 7 Friedrichs, K. O., Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, Math. Ann., Vol. 109, 1934, pp. 465–487. 8 Friedrichs, K. O., Über die ausgezeichnete Randbedingung in der Spektraltheorie der halbbeschränkten gewöhnlichen Differentialoperatoren zweiter Ordnung, Math. Ann., Vol. 112, 1936, pp. 1–23. 9 Titchmarsh, E. C., Eigenfunction Expansions Associated With Second-Order Differential Equations, The Clarendon Press, Oxford, 1946; see references, especially to Hilbert. 10 Friedrichs, K. O., Criteria for the discrete character of the spectra of ordinary differential equations, R. Courant Anniversary Volume, Interscience Publishers, New York, 1948, pp. 145–160. 11 Hartman, P., On differential equations with non-oscillatory eigenfunctions, Duke Math. J., Vol. 15, 1948, pp. 697–709. 12 Hartman, P., and Putnam, C. R., The least cluster point of the spectrum of boundary value problems, Amer. J. Math., Vol. 70, 1948, pp. 849–855. 13 Hille, E., Non-oscillation theorems, Trans. Amer. Math. Soc., Vol. 64, 1948, pp. 234–252. 14 Hartman, P., and Wintner, A., Oscillatory and non-oscillatory linear differential equations, Amer. J. Math., Vol. 71, 1949, pp. 627–649. 15 Hartman, P., A characterization of the spectra of one-dimensional wave equations, Amer. J. Math., Vol. 71, 1949, pp. 915–920. 16 Friedrichs, K. O., Criteria for discrete spectra, Comm. Pure Appl. Math., Vol. 3, 1950, pp. 439–449. 17 Rellich, F., Spectral theory of a second-order ordinary differential equation, Lecture Notes, New York University, 1950-1951. 18 Hartman, P. and Wintner, A., On the essential spectra of singular eigenvalue problems, Amer. J. Math., Vol. 72, 1950, pp. 545–552. 19 Wolfson, K. G., On the spectrum of a boundary value problem with two singular endpoints, Amer. J. Math., Vol. 72, 1950, pp. 713–719. 20 Sears, D. B., On the spectrum of a certain differential equation, J. London Math. Soc., Vol. 26, 1951, pp. 205–210. 21 Rellich, F., Halbbeschränkte gewöhnliche Differentialoperatoren zweiter Ordnung, Math. Ann., Vol. 122, 1951, pp. 343–368. 22 Coddington, E. A., and Levinson, N., On the nature of the spectrum of singular second order linear differential equations, Canadian J. Math., Vol. 3, 1951, pp. 335–338. 23 Heinz, E., Zur Theorie der Hermiteschen Operatoren des Hilbertschen Raumes, Nachr. Akad. Wiss. Göttingen, Math.-Phys. Kl. Math.-Phys.-Chem. Abt., 1951, pp. 1–4. Citing Literature Volume12, Issue3August 1959Pages 523-542 ReferencesRelatedInformation" @default.
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