NDLI: Description of generalized resolvents and characteristic matrices of differential operators in terms of the boundary parameter

Content Provider	Springer Nature Link
Author	Mogilevskii, V. I.
Copyright Year	2011
Abstract	We supplement and further develop well-known results due to Shtraus on the generalized resolvents and spectral functions of the minimal operator L $_{0}$ generated by a formally selfadjoint differential expression of even order with operator coefficients given on the interval [0, b〉, where b≤∞. Our approach is based on the notion of a disintegrating boundary triple, which allows us to establish a relation between the Shtraus method and boundary-value problems with spectral parameter in the boundary condition. In particular, we obtain a parametrization of all the characteristic matrices Ω(λ) of the operator L $_{0}$ in terms of the spectral parameter corresponding to a boundary-value problem. Such a parametrization is given as a block representation of the matrix Ω(λ), as well as by formulas similar to Krein’s well-known formula for generalized resolvents.
Starting Page	548
Ending Page	570
Page Count	23
File Format	PDF
ISSN	00014346
Journal	Mathematical Notes
Volume Number	90
Issue Number	3-4
e-ISSN	15738876
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2011-10-29
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	differential operator of even order minimal operator self-adjoint operator generalized resolvent characteristic matrix boundary-value problem deficiency index boundary triple holomorphic function Nevanlinna function Weyl function Mathematics
Content Type	Text
Resource Type	Article

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