Zusammenfassung
The following lines give a brief and simple proof of the existence of characteristic functions for the symmetric kernel1), and then point out that the complete sets of such functions which arise from the usual self-adjoint differential equations with self adjoint boundary conditions are closed, not only with respect to continuous functions, but also with respect to summable functions.
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Literatur
Memorie della R. Ace. dei Lincei 18 (1883), pp. 581–586.
Annales de la Faculté des Sciences de Toulouse (2) 3 (1901).
Cf. also Westfall: Bull. Amer. Math. Soc. 15 (1908), pp. 76–78;
Steckloff: Mémoires de l’Académie Impériale des Sciences de St. Pétersbourg 30 (1911), Nr. 4.
Grundzüge einer allgemeinen Theorie der linearen Integralgleichungen, Zweite Mitteilung, Nachrichten d. K. Ges. d. Wiss. zu Göttingen 1904, Heft 3, p. 222
Note on closure of orthogonal sets, Bull. Amer. Math. Soc. 27 (1921), pp. 165–169.
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© 1982 Springer-Verlag Berlin Heidelberg
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Kellogg, O.D. (1982). On the existence and closure of sets of characteristic functions. In: Festschrift. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61810-9_36
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DOI: https://doi.org/10.1007/978-3-642-61810-9_36
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