Vadim Mogilevskii
Boundary relations and boundary conditions for general (not necessarily definite) canonical systems with possibly unequal deficiency indices.
Tue, 09/13/2011 - 15:01 — SomNambulAuthors: Vadim Mogilevskii
Subjects: Functional Analysis
AbstractWe investigate in the paper general (not necessarily definite) canonical
systems of differential equation in the framework of extension theory of
symmetric linear relations. For this aim we first introduce the new notion of a
boundary relation $\G:\gH^2\to\HH$ for $A^*$, where $\gH$ is a Hilbert space,
$A$ is a symmetric linear relation in $\gH, \cH_0$ is a boundary Hilbert space
and $\cH_1$ is a subspace in $\cH_0$.Minimal spectral functions of an ordinary differential operator.
Thu, 10/07/2010 - 15:01 — SomNambulAuthors: Vadim Mogilevskii
Subjects: Functional Analysis
AbstractLet $l[y]$ be a formally selfadjoint differential expression of an even order
on the interval $[0,b> \;(b\leq \infty)$ and let $L_0$ be the corresponding
minimal operator. By using the concept of a decomposing boundary triplet we
consider the boundary problem formed by the equation $l[y]-\l y=f\;(f\in
L_2[0,b>)$ and the Nevanlinna $\l$-depending boundary conditions with constant
values at the regular endpoint 0.On generalized resolvents and characteristic matrices of differential operators.
Tue, 09/22/2009 - 14:09 — SomNambulAuthors: Vadim Mogilevskii
Subjects: Functional Analysis
AbstractThe main objects of our considerations are differential operators generated
by a formally selfadjoint differential expression of an even order on the
interval $[0,b> (b\leq \infty)$ with operator valued coefficients. We
complement and develop the known Shtraus' results on generalized resolvents and
characteristic matrices of the minimal operator $L_0$.
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