Abstract
We propose a method for investigation of both correctness of the equivariant problem and the spectrum of the corresponding operator.
Similar content being viewed by others
References
V. P. Burskii, “On a commutative diagram, traces of solutions, and the spectrum of the operator of a boundary-value problem for the Laplace equation in a circle,” in:Nonlinear Boundary-Value Problems [in Russian], Institute of Applied Mathematics and Mechanics, Ukrainian Academy of Sciences, Issue 2, Naukova Dumka, Kiev (1990), pp. 13–19.
Nguyen Kuok Zan, “On boundary-value problems for the Laplace equation in a circle,”Ukr. Mat. Zh.,24, No. 6, 763–771 (1972).
V. I. Gorbachuk, “On boundary-value problems for elliptic differential equations,”Dokl. Akad. Nauk SSSR. Ser. A, No. 1, 7–11 (1981).
M. I. Vishik, “General boundary-value problems for elliptic differential equations,”Tr. Mosk. Mat. Obshch.,1, 187–246 (1952).
L. Hörmander,On the Theory of General Partial Differential Operators [Russian translation], Inostrannaya Literatura, Moscow (1959).
Yu. M. Berezanskii,Decomposition in Eigenfunctions of Self-Conjugate Operators [in Russian], Naukova Dumka, Kiev (1965).
A. A. Dezin,General Questions of the Theory of Boundary-Value Problems [in Russian], Nauka, Moscow (1980).
V. I. Gorbachuk and M. L. Gorbachuk,Boundary-Value Problems for Differential-Operator Equations [in Russian], Naukova Dumka, Kiev (1984).
A. N. Kochubei, “On symmetric operators commuting with a family of unitary operators,”Funkts. Anal. Prilozh.,13, No. 4, 77–78 (1979).
V. P. Burskii, “A commutative diagram connected with a differential operator in a domain,”Ukr. Mat. Zh.,43, No. 12, 1703–1709 (1991).
V. P. Burskii, “Boundary properties of L2-solutions of linear differential equations and the ‘equation-domain’ duality,”Dokl. Akad. Nauk SSSR,309, No. 5, 1036–1039 (1989).
S. Helgason,Croups and Geometric Analysis [Russian translation], Mir, Moscow (1987).
N. Ya. Vilenkin,Special Functions and Theory of Group Representation [in Russian], Nauka, Moscow (1991).
A. A. Kirilov,Elements of Representation Theory [in Russian], Nauka, Moscow (1978).
H. Bateman and A. Erdëlyi,Higher Transcendental Functions, Vol. 2, McGraw-Hill, New-York (1953).
H. Watson,Theory of Bessel Functions [Russian translation], Vol. 1, Inostrannaya Literatura, Moscow (1949).
Author information
Authors and Affiliations
Additional information
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 158–169, February, 1999.
Rights and permissions
About this article
Cite this article
Burskii, V.P. On equivariant extensions of a differential operator by the example of the Laplace operator in a circle. Ukr Math J 51, 172–184 (1999). https://doi.org/10.1007/BF02513471
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02513471