2003 Colloquium on Differential Equations and Applications,
Maracaibo, Venezuela.
Electron. J. Diff. Eqns., Conference 13, 2005, pp. 101112.
The division method for subspectra of selfadjoint differential
vectoroperators
Maksim Sokolov
Abstract:
We discuss the division method for subspectra which appears to be
one of the key approaches in the study of spectral properties of
selfadjoint differential vectoroperators, that is operators
generated as a direct sum of selfadjoint extensions on an
EverittMarkusZettl multiinterval system. In the current work we
show how the division method may be applied to obtain the ordered
spectral representation and Fourierlike decompositions for
selfadjoint differential vectoroperators, after which we obtain
the analytical decompositions for the measurable (relative to a
spectral parameter) generalized eigenfunctions of a selfadjoint
differential vectoroperator.
Published May 30, 2005.
Math Subject Classifications: 34L05, 47B25, 47B37, 47A16.
Key Words: Vectoroperator; 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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