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2005 | 3 | 4 | 627-643
Tytuł artykułu

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

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Treść / Zawartość
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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.
Wydawca
Czasopismo
Rocznik
Tom
3
Numer
4
Strony
627-643
Opis fizyczny
Daty
wydano
2005-12-01
online
2005-12-01
Twórcy
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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_BF02475623
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