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

Open Mathematics (2005)

- Volume: 3, Issue: 4, page 627-643
- ISSN: 2391-5455

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topMaksim Sokolov. "Self-adjoint differential vector-operators and matrix Hilbert spaces I." Open Mathematics 3.4 (2005): 627-643. <http://eudml.org/doc/268841>.

@article{MaksimSokolov2005,

abstract = {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.},

author = {Maksim Sokolov},

journal = {Open Mathematics},

keywords = {34L05; 47B25; 47B37; 47A16},

language = {eng},

number = {4},

pages = {627-643},

title = {Self-adjoint differential vector-operators and matrix Hilbert spaces I},

url = {http://eudml.org/doc/268841},

volume = {3},

year = {2005},

}

TY - JOUR

AU - Maksim Sokolov

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

JO - Open Mathematics

PY - 2005

VL - 3

IS - 4

SP - 627

EP - 643

AB - 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.

LA - eng

KW - 34L05; 47B25; 47B37; 47A16

UR - http://eudml.org/doc/268841

ER -

## References

top- [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. Zbl1045.47016
- [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. Zbl1078.34066
- [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 Zbl1086.34067
- [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. Zbl0723.34022
- [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). Zbl0982.47032
- [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 Zbl1049.47043
- [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. Zbl0128.34803

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