Analog of the Krein Formula for Resolvents of Normal Extensions of a Prenormal Operator
- 28 Downloads
We prove a formula that relates resolvents of normal operators that are extensions of a certain prenormal operator. This formula is an analog of the Krein formula for resolvents of self-adjoint extensions of a symmetric operator. We describe properties of the defect subspaces of a prenormal operator.
KeywordsNormal Operator Symmetric Operator Normal Extension Defect Subspace Krein Formula
Unable to display preview. Download preview PDF.
- 1.M. L. Horbachuk and V. I. Horbachuk, “Theory of self-adjoint extensions of symmetric operators. Entire operators and boundary-value problems,” Ukr. Mat. Zh., 46, No. 1-2, 55–62 (1994).Google Scholar
- 2.M. L. Horbachuk and V. I. Horbachuk, Boundary-Value Problems for Operator Differential Equations [in Russian], Naukova Dumka, Kiev (1984).Google Scholar
- 3.E. A. Coddington, “Normal extension of formally normal operators,” Pacif. J. Math., 10, 1203–1209 (1960).Google Scholar
- 4.M. I. Vishik, “On general boundary-value problems for elliptic differential equations,” Tr. Mosk. Mat. Obshch., 1, 187–246 (1952).Google Scholar
- 5.V. É. Lyantse and O. G. Storozh, Methods of the Theory of Unbounded Operators [in Russian], Naukova Dumka, Kiev (1983).Google Scholar
- 6.A. V. Kuzhel', “An analog of Krein formula for resolvents of nonself-adjoint extensions of an Hermitian operator,” Teor. Funkts. Funkts. Anal. Prilozhen., Issue 36, 49–55 (1981).Google Scholar
- 7.A. V. Kuzhel and S. A. Kuzhel, Regular Extensions of Hermitian Operators, VSP, Utrecht (1998).Google Scholar
- 8.M. E. Dudkin, “Singularly perturbed normal operators,” Ukr. Mat. Zh., 51, No. 8, 1045–1053 (1999).Google Scholar
- 9.V. D. Koshmanenko, Singular Bilinear Forms in Perturbation Theory for Self-Adjoint Operators [in Russian], Naukova Dumka, Kiev (1993).Google Scholar
- 10.M. G. Krein, “Theory of self-adjoint extensions of positive Hermitian operators and its applications,” Mat. Sb., 20, No. 3, 431–490 (1947).Google Scholar
- 11.I. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Spaces [in Russian], Nauka, Moscow (1966).Google Scholar