"2003 Colloquium on Differential Equations and Applications,
Maracaibo, Venezuela.
Electronic Journal of Differential Equations,
Conference 13, 2005, pp. 101-112.
Title: The division method for subspectra of self-adjoint differential
vector-operators
Author: Maksim Sokolov (National Univ. of Uzbekistan, Uzbekistan)
Abstract:
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.