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Keywords
(9)
Hilbert Space
Internal Structure
Selfadjoint Extension
Spectral Measure
Spectral Properties
Spectral Representation
Spectral Resolution
Spectral Theorem
Spectral Theory
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Introduction to the spectral theory of selfadjoint differential vectoroperators
Introduction to the spectral theory of selfadjoint differential vectoroperators,MAKSIM S. SOKOLOV
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Introduction to the spectral theory of selfadjoint differential vectoroperators
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MAKSIM S. SOKOLOV
We study the
spectral theory
of operators, generated as direct sums of selfadjoint extensions of quasidifferential minimal operators on a multiinterval set (selfadjoint vectoroperators), acting in a Hilbert space. Spectral theorems for such operators are discussed, the structure of the ordered
spectral representation
is investigated for the case of differential coordinate operators. One of the main results is the construction of spectral resolutions. Finally, we study the matters connected with analytical decompositions of generalized eigenfunctions of such vectoroperators and build a matrix
spectral measure
leading to the matrix
Hilbert space
theory. Results, connected with other
spectral properties
of selfadjoint vectoroperators, such as the introduction of the identity resolution and the spectral multiplicity have also been obtained. Vectoroperators have been mainly studied by W.N. Everitt, L. Markus and A. Zettl. Being a natural continuation of EverittMarkusZettl theory, the presented results reveal the
internal structure
of selfadjoint vectoroperators and are essential for the further study of their spectral properties.
Published in 2004.
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References
(6)
MultiInterval Linear Ordinary Boundary Value Problems and Complex Symplectic Algebra
(
Citations: 11
)
W. Everitt
,
L. Markus
Published in 2001.
AN ABSTRACT APPROACH TO SOME SPECTRAL PROBLEMS OF DIRECT SUM DIFFERENTIAL OPERATORS
(
Citations: 5
)
MAKSIM S. SOKOLOV
Onedimensional Schrödinger operators with interactions singular on a discrete set
(
Citations: 38
)
W. Kirsch
,
F. Gesztesy
Journal:
Journal Fur Die Reine Und Angewandte Mathematik  J REINE ANGEW MATH
, vol. 1985, no. 362, pp. 2850, 1985
Linear Operators Generated by a Countable Number of Quasidifferential Expressions
(
Citations: 5
)
R. R. Ashurov
,
W. N. Everitt
Journal:
Applicable Analysis
, vol. 81, no. 6, pp. 14051425, 2002
Linear quasidifferential operators in locally integrable spaces on the real line
(
Citations: 6
)
R. R. Ashurov
,
W. N. Everitt
Journal:
Proceedings of The Royal Society of Edinburgh Section Amathematics  PROC ROY SOC EDINBURGH SECT A
, vol. 130, no. 04, 2000