Abstract
Sufficient conditions are obtained for the self-conjugacy of certain operators generated on a semiaxis or a complete axis by a differential expression of the form l[y]=y″+Ay−q(t)y, where A is a self-conjugate operator bounded below in a separable Hilbert space H, and, for almost all t, q(t) is a bounded self-conjugate operator in H, locally summable with the square of the norm.
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Literature cited
Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Conjugate Operators [in Russian], Naukova Dumka, Kiev (1965).
V. I. Gorbachuk and M. L. Gorbachuk, “Spectral theory of linear differential equations with unbounded operator coefficients,” Ukrainsk. Mat. Zh.,23, No. 1, 3–14 (1971).
L. I. Vainerman, “The existence of decision functions for a second-order differential equation with operator coefficients, Dop. Akad. Nauk URSR, Ser. A,1, 3–5 (1972).
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Additional information
Translated from Matematicheskie Zametki, Vol. 20, No. 5, pp. 703–708, November, 1976.
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Vainerman, L.I. Self-conjugacy of abstract differential operators of the hyperbolic type. Mathematical Notes of the Academy of Sciences of the USSR 20, 954–957 (1976). https://doi.org/10.1007/BF01146917
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DOI: https://doi.org/10.1007/BF01146917