Abstract
We study the dependence of the rate of growth of the extended spectral measure of a self-adjoint operator at infinity on the order of singularity of the vector on which this measure is considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Yu. L. Shmul’yan, “Extended resolvents and extended spectral functions of an Hermitian operator,” Mat. Sb., 84, No. 3, 440–456 (1971).
Yu. M. Berezanskii, Self-Adjoint Operators in Spaces of Functions of Infinitely Many Variables [in Russian], Naukova Dumka, Kiev (1978).
V. I. Gorbachuk and M. L. Gorbachuk, Boundary-Value Problems for Operator-Differential Equations [in Russian], Naukova Dumka, Kiev (1984).
Yu. M. Berezanskii, Expansion in Eigenfunctions of Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1965).
V. I. Gorbachuk, “Theorems of the Wiener-Paley type for normal operators and their applications,” in: Nonlinear Boundary-Value Problems. 2 [in Russian], Naukova Dumka, Kiev (1990), pp. 19–25.
Additional information
Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 4, pp. 510–516, April, 1997.
Rights and permissions
About this article
Cite this article
Gorbachuk, M.L., Gorbachuk, V.I. Behavior of the extended spectral measure of a self-adjoint operator at infinity. Ukr Math J 49, 561–568 (1997). https://doi.org/10.1007/BF02487318
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02487318