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10.—Generalisation of Some Statements by Kodaira

  • Christer Bennewitz (a1)

Synopsis

This paper presents a generalisation of earlier results on the dimension of the space of integrable-square solutions of the ordinary linear differential equation Su = λTu, where S and T are formally symmetric ordinary differential operators and λ is a spectral parameter.

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References

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[1]Everitt, W. N., 1959. Integrable-square solutions of ordinary differential equations. Q. Jl Math., 10, 145155.
[2]Kimura, T. and Takahasi, M., 1965. Sur les opérateurs différentiels ordinaires linéaires formellement autoadjoints I. Funkcialoj Ekvacioj, Ser. Int., 7, 3590.
[3]Kodatra, K., 1950. On ordinary differential equations of any even order and the corresponding eigenfunction expansions. Am. J. Math., 72, 502544.
[4]Pleijel, A., 1969. Complementary remarks about the limit point and limit circle theory. Ark. Mat., 8, 4547.
[5]Weyl, H., 1910. Über gewöhnlicke Differentialgleichungen mit Singularitäten und die zugehörigen Entwicklungen willkürlicher Funktionen. Math. Annin, 68, 220–269. (Also in Selecta Hermann Weyl, 1956. Basel: Birkäuser Verlag.)

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