2003 Colloquium on Differential Equations and Applications, Maracaibo, Venezuela.
Electron. J. Diff. Eqns., Conference 13, 2005, pp. 101-112.

The division method for subspectra of self-adjoint differential vector-operators

Maksim Sokolov

We discuss the division method for subspectra which appears to be one of the key approaches in the study of spectral properties of self-adjoint differential vector-operators, that is operators generated as a direct sum of self-adjoint extensions on an Everitt-Markus-Zettl multi-interval system. In the current work we show how the division method may be applied to obtain the ordered spectral representation and Fourier-like decompositions for self-adjoint differential vector-operators, after which we obtain the analytical decompositions for the measurable (relative to a spectral parameter) generalized eigenfunctions of a self-adjoint differential vector-operator.

Published May 30, 2005.
Math Subject Classifications: 34L05, 47B25, 47B37, 47A16.
Key Words: Vector-operator; cyclic vector; spectral representation; ordered representation; multiplicity; unitary transformation.

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Maksim S. Sokolov
ICTP Affiliated Center
Mechanics and Mathematics Department
National University of Uzbekistan
Tashkent 700095, Uzbekistan
email: sokolovmaksim@hotbox.ru

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