Abstract
Various classes of extensions of symmetric operators with equal (finite or infinite) defect numbers are described in terms of abstract boundary conditions. The dual problem of the description of extensions of a symmetric binary relation is also considered.
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Literature cited
J. W. Calkin, “Abstract symmetric boundary conditions,” Trans. Amer. Math. Soc.,45, No. 3, 369–442 (1939).
N. Dunford and J. Schwartz, Linear Operators, Vol. 2, Interscience (1958).
A. V. Shtraus, “Some questions of the theory of extensions of symmetric nonself-adjoint operators,” Transactions of the 2nd Scientific Conference, Kafedr Fed. Univ. Povolzh', No. 1, Kuibyshev, 121–124 (1962).
M. L. Gorbachuk, A. N. Kochubei, and M. A. Rybak, “Dissipative extensions of operators in a space of vector functions,” Dokl. Akad. Nauk SSSR,205, No. 5, 1029–1032 (1972).
M. L. Gorbuchuk, A. N. Kochubei, and M. A. Rybak, “Some classes of extensions of differential operators in a space of vector functions,” in: Application of Functional Analysis to Problems of Mathematical Physics [in Russian], Kiev (1973), pp. 56–82.
F. S. Rofe-Beketov, “Self-adjoint extensions of differential operators in a space of vector functions,” Theory of Functions, Funktsional'. Analiz i Ego Prilozhen., No. 8, 3–24 (1969).
M. I. Vishik, “General boundary value problems for elliptic differential equations,” Tr. Moscow Matern. Ob.,1, 187–246 (1952).
M. L. Gorbachuk and A. N. Kochubei, “Self-adjoint boundary value problems for certain classes of differential operator equations of second order,” Dokl. Akad. Nauk SSSR,201, No. 5, 1029–1032 (1971).
A. V. Shtraus, “Extensions and characteristic functions of a symmetric operator,” Izv. Akad. Nauk SSSR, Ser. Matem.,32, No. 1, 186–207 (1968).
M. O. Talyush, “The typical structure of dissipative operators,” Dop. Akad. Nauk URSR, No. 11, 993–996 (1973).
R. Gunning and H. Rossi, Analytic Functions of Several Complex Variables, Prentice-Hall (1965).
H. Bourbaki, Integration. Vector Integration. Haar Measure, Convolutions, and Representations, Hermann, Paris (1952).
C. Bennewitz, “Symmetric relations on a Hilbert space,” Lecture Notes Math.,280, 212–218 (1972).
E. A. Coddington, “Extension theory of formally normal and symmetric subspaces,” Memoirs Amer. Math. Soc.,134, 1–80 (1973).
Additional information
Translated from Matematicheskii Zametki, Vol. 17, No. 1, pp. 41–48, January, 1975.
The author thanks M. L. Gorbachuk for useful observations.
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Kochubei, A.N. Extensions of symmetric operators and symmetric binary relations. Mathematical Notes of the Academy of Sciences of the USSR 17, 25–28 (1975). https://doi.org/10.1007/BF01093837
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DOI: https://doi.org/10.1007/BF01093837