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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Eigenfunction expansions associated with singular differential operators

Author: Joanne Elliott
Journal: Trans. Amer. Math. Soc. 78 (1955), 406-425
MSC: Primary 36.0X
MathSciNet review: 0068701
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  • [1] William Feller, The parabolic differential equations and the associated semi-groups of transformations, Ann. of Math. (2) 55 (1952), 468–519. MR 0047886
  • [2] Einar Hille, Functional Analysis and Semi-Groups, American Mathematical Society Colloquium Publications, vol. 31, American Mathematical Society, New York, 1948. MR 0025077
  • [3] 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 0033421
  • [4] Norman Levinson, A simplified proof of the expansion theorem for singular second order linear differential equations, Duke Math. J. 18 (1951), 57–71. MR 0041313
  • [5] Ruth Lind Potter, On self-adjoint differential equations of second order, Pacific J. Math. 3 (1953), 467–491. MR 0056156
  • [6] E. C. Titchmarsh, Eigenfunction Expansions Associated with Second-Order Differential Equations, Oxford, at the Clarendon Press, 1946 (German). MR 0019765
  • [7] -, Introduction to the theory of Fourier integrals, Oxford, 1937.
  • [8] Hermann Weyl, Über gewöhnliche Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen, Math. Ann. 68 (1910), no. 2, 220–269 (German). MR 1511560, 10.1007/BF01474161
  • [9] Einar Hille, The abstract Cauchy problem and Cauchy’s problem for parabolic differential equations, J. Analyse Math. 3 (1954), 81–196. MR 0062934

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Article copyright: © Copyright 1955 American Mathematical Society