Parametrizations of Titchmarsh’s $m(\lambda )$-functions in the limit circle case
HTML articles powered by AMS MathViewer
- by Charles T. Fulton PDF
- Trans. Amer. Math. Soc. 229 (1977), 51-63 Request permission
Abstract:
For limit-circle eigenvalue problems the so-called $’m(\lambda )’$-functions of Titchmarsh [15] are introduced in such a fashion that their parametrization is built into the definition.References
- Earl A. Coddington and Norman Levinson, Theory of ordinary differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1955. MR 0069338
- Nelson Dunford and Jacob T. Schwartz, Linear operators. Part II: Spectral theory. Self adjoint operators in Hilbert space, Interscience Publishers John Wiley & Sons, New York-London, 1963. With the assistance of William G. Bade and Robert G. Bartle. MR 0188745 C. Fulton, Parametrizations of Titchmarsh’s $m(\lambda )$-functions in the limit circle case, Dissertation, Rheinisch-Westfälischen Tech. Hochschule Aachen, 1973.
- Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
- GĂĽnter Hellwig, Differential operators of mathematical physics. An introduction, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1967. Translated from the German by Birgitta Hellwig. MR 0211292
- Einar Hille, Lectures on ordinary differential equations, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. MR 0249698 K. Jörgens, Spectral theory of 2nd-order ordinary differential operators, Lecture Notes, Matematisk Institut, Aarhus Universitet, Denmark, 1962-63.
- Kunihiko Kodaira, The eigenvalue problem for ordinary differential equations of the second order and Heisenberg’s theory of $S$-matrices, Amer. J. Math. 71 (1949), 921–945. MR 33421, DOI 10.2307/2372377
- M. A. Neumark, Lineare Differentialoperatoren, Akademie-Verlag, Berlin, 1960 (German). MR 0216049
- Franz Rellich, Halbbeschränkte gewöhnliche Differentialoperatoren zweiter Ordnung, Math. Ann. 122 (1951), 343–368 (German). MR 43316, DOI 10.1007/BF01342848 —, Spectral theory of a second-order differential equation, Lecture notes, New York Univ., 1951.
- D. B. Sears, Integral transforms and eigenfunction theory, Quart. J. Math. Oxford Ser. (2) 5 (1954), 47–58. MR 62310, DOI 10.1093/qmath/5.1.47
- D. B. Sears and E. C. Titchmarsh, Some eigenfunction formulae, Quart. J. Math. Oxford Ser. (2) 1 (1950), 165–175. MR 37436, DOI 10.1093/qmath/1.1.165
- Marshall Harvey Stone, Linear transformations in Hilbert space, American Mathematical Society Colloquium Publications, vol. 15, American Mathematical Society, Providence, RI, 1990. Reprint of the 1932 original. MR 1451877, DOI 10.1090/coll/015
- E. C. Titchmarsh, Eigenfunction expansions associated with second-order differential equations. Part I, 2nd ed., Clarendon Press, Oxford, 1962. MR 0176151
- E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford, at the Clarendon Press, 1946 (German). MR 0019765
- E. C. Titchmarsh, On expansions in eigenfunctions. IV, Quart. J. Math. Oxford Ser. 12 (1941), 33–50. MR 5232, DOI 10.1093/qmath/os-12.1.33
- Hermann Weyl, Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen, Math. Ann. 68 (1910), no. 2, 220–269 (German). MR 1511560, DOI 10.1007/BF01474161
- KĂ´saku Yosida, Lectures on differential and integral equations, Pure and Applied Mathematics, Vol. X, Interscience Publishers, New York-London, 1960. MR 0118869
Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 229 (1977), 51-63
- MSC: Primary 34B20
- DOI: https://doi.org/10.1090/S0002-9947-1977-0450657-6
- MathSciNet review: 0450657