Self-adjoint differential vector-operators and matrix Hilbert spaces I

• Autorzy: Maksim Sokolov
• Języki publikacji: EN

Abstrakty

EN

In the current work a generalization of the famous Weyl-Kodaira inversion formulas for the case of self-adjoint differential vector-operators is proved. A formula for spectral resolutions over an analytical defining set of solutions is discussed. The article is the first part of the planned two-part survey on the structural spectral theory of self-adjoint differential vector-operators in matrix Hilbert spaces.

Słowa kluczowe

EN

Self-adjoint differential vector-operators; (direct sum operators); multi-interval quasi-differential systems; matrix spectral measure; Weyl-Kodaira inversion theorem; 34L05; 47B25; 47B37; 47A16

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2005
• Tom: 3
• Numer: 4
• Strony: 627-643

Daty

wydano

2005-12-01

online

2005-12-01

Twórcy

autor

Maksim Sokolov

• The National University of Uzbekistan

Bibliografia

• [1] M.S. Sokolov: “An abstract approach to some spectral problems of direct sum differential operators”, Electronic. J. Diff. Eq., Vol. 75, (2003), pp. 1–6.
• [2] M.S. Sokolov: “On some spectral properties of operators generated by multi-interval quasi-differential systems”, Methods Appl. Anal., Vol. 10(4), (2004), pp. 513–532.
• [3] R.R. Ashurov and M.S. Sokolov: “On spectral resolutions connected with self-adjoint differential vector-operators in a Hilbert space”, Appl. Anal., Vol. 84(6), (2005), pp. 601–616. http://dx.doi.org/10.1080/00036810500048160
• [4] W.N. Everitt and A. Zettl: “Quasi-differential operators generated by a countable number of expressions on the real line”, Proc. London Math. Soc., Vol. 64(3), (1992), pp. 524–544.
• [5] W.N. Everitt and L. Markus: “Multi-interval linear ordinary boundary value problems and complex symplectic algebra”, Mem. Am. Math. Soc., Vol. 715, (2001).
• [6] R.R. Ashurov and W.N. Everitt: “Linear operators generated by a countable number of quasi-differential expressions”, Appl. Anal., Vol. 81(6), (2002), pp. 1405–1425. http://dx.doi.org/10.1080/0003681021000035506
• [7] M.A. Naimark: Linear differential operators, Ungar, New York, 1968.
• [8] M. Reed and B. Simon: Methods of modern mathematical physics, Vol. 1: Functional Analysis, Academic Press, New York, 1972.
• [9] N. Dunford and J.T. Schwartz: Linear operators, Vol. 2: Spectral Theory, Interscience, New York, 1964.

Identyfikatory

DOI

10.2478/BF02475623