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References
S.Bochner, Sturm-Liouville and heat equations whose eigenfunctions are ultraspherical polynomials or associated Bessel functions, Proc. Conf. Diff. Eq., Maryland (1956).
B.L.J.Braaksma and H.S.V.de Snoo, Internal report, Dept. of Math., University of Groningen (1974).
H. Chébli, Sur la positivité des opérateurs de "translation généralisée" associés à un opérateur de Sturm-Liouville sur ]0,∞[, C.R. Acad. Sc. Paris, 275, 601–604 (1972).
H. Chébli, Sur la positivité des opérateurs de "translation généralisée" associés à un opérateur de Sturm-Liouville sur ]0,∞[, Séminaire de Théorie Spectrale, Strasbourg, 1972–73.
H.Chébli, Sur un théorème de Paley-Wiener associé à la décomposition spectrale d'un opérateur de Sturm-Liouville sur ]0,∞[, Report Institut de Recherche Math. Avancée Strasbourg (1974).
T.M. Cherry, On expansions in eigenfunctions, particularly in Bessel functions, Proc. London Math. Soc. 51, 14–45 (1949–50).
J. Delsarte, Sur une extension de la formule de Taylor, Journal de Math. Pur. App. 17, 213–231 (1936).
M. Flensted-Jensen, Paley-Wiener type theorems for a differential operator connected with symmetric spaces, Arkiv för Matematik 10, 143–162 (1972).
M. Flensted-Jensen and T.H. Koornwinder, The convolution structure for Jacobi function expansions, Arkiv för Matematik 11, 245–262 (1973).
V. Hutson and J.S. Pym, Generalized translations associated with a differential operator, Proc. London Math. Soc. 24, 548–576 (1972).
V. Hutson and J.S. Pym, Measure algebras associated with a second order differential operator, Journ. Functional An. 12, 68–96 (1973).
N. Leblanc, Classification des algèbres de Banach associées aux opérateurs différentiels de Sturm-Liouville, Journ. Functional An. 2, 52–72 (1968).
N.Leblanc, Algèbres de Banach associées à un opérateur différentiel de Sturm-Liouville, Springer lecture notes no. 336, 40–50 (1973).
B.M.Levitan, The application of generalized displacement operators to linear differential equations of the second order, Translation no. 59, Amer. Math. Soc. (1950).
B.M.Levitan, Generalized translation operators and some of their applications, Jerusalem, 1964.
M.H.Protter and H.F.Weinberger, Maximum principles in differential equations, Englewood Cliffs, 1967.
B. Riemann, Gesammelte Mathematische Werke, Dover publ., New York, 1953.
H.S.V. de Snoo, Inversion theorems for some generalized Laplace transforms I, II, Proc. Kon. Nederl. Akad. Wet., Ser. A, 73, 222–244 (1970).
G.N.Watson, A treatise on the theory of Bessel functions, 2nd ed., Cambrdige, 1966.
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Braaksma, B.L.J., de Snoo, H.S.V. (1974). Generalized translation operators associated with a singular differential operator. In: Sleeman, B.D., Michael, I.M. (eds) Ordinary and Partial Differential Equations. Lecture Notes in Mathematics, vol 415. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0065512
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DOI: https://doi.org/10.1007/BFb0065512
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