Some analytic properties of the Weyl function of a closed linear relation
Journal Title: Карпатські математичні публікації - Year 2018, Vol 10, Issue 1
Abstract
Let L and L0, where L is an expansion of L0, be closed linear relations (multivalued operators) in a Hilbert space H. In terms of abstract boundary operators (i.e. in the form which in the case of differential operators leads immediately to boundary conditions) some analytic properties of the Weyl function M(λ) corresponding to a certain boundary pair of the couple (L,L0), are studied. In particular, applying Hilbert resolvent identity for relations, the criterion of invertibility in the algebra of bounded linear operators in H for transformation M(λ)−M(λ0) in certain small punctured neighbourhood of λ0 is established. It is proved that in this case λ0 is a first-order pole for the operator-function (M(λ)−M(λ0))−1. The corresponding residue and Laurent series expansion are found. Under some additional assumptions, the behaviour of so called γ-field Zλ (being an operator-function closely connected to M(λ)) as λ→−∞ is investigated.
Authors and Affiliations
O. G. Storozh
Keywords
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- EP ID EP532887
- DOI 10.15330/cmp.10.1.197-205
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