Results 271 to 280 of about 673 (299)
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Reduction of Generalized Resolvents of Linear Operator Functions
Integral Equations and Operator Theory, 2004In this paper, linear operator functions, that is, functions of the form \(L(\lambda)=T-\lambda S\), \(\lambda\in \mathbb C\), where \(S\) and \(T\) are linear bounded operators between Banach spaces, are studied. A generalized (or relative) inverse of \(L\), denoted by \(L^+\), is called a generalized resolvent of \(L\) if it is smooth at \(0\) and ...
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On semi-groups of operators and the resolvents of their generators
Mathematical Proceedings of the Cambridge Philosophical Society, 1969In a recent paper (4) concerned with the study of ‘fundamental operators’, we have obtained results involving the resolvents of the generators of some semi-groups of operators in Lp (− ∞, ∞). In this paper we consider those results which, under suitable conditions, can be extended to cases where the resolvents do not necessarily form a class of ...
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Extensions and generalized resolvents of closed dissipative operators
Mathematical Notes of the Academy of Sciences of the USSR, 1974Let B be a closed dissipative operator in a Hilbert space ℋ with an arbitrary domain of definition. We investigate briefly the problem of describing all the closed (and, in particular, the closed maximal) dissipative extensions B of the operator B. Following this we introduce the concept of a generalized resolvent of a closed dissipative operator with ...
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Singularities of the resolvent at the thresholds of a stratified operator: a general method
Mathematical Methods in the Applied Sciences, 2004AbstractOur problem is about propagation of waves in stratified strips. The operators are quite general, a typical example being a coupled elasto‐acoustic operator H defined in ℝ2 × I where I is a bounded interval of ℝ with coefficients depending only on z∈I.
Chabi Gado, Bio Soumarou +2 more
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On Generation of Family of Resolving Operators for a Distributed Order Equation Analytic in Sector
Journal of Mathematical Sciences, 2022zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Generalized resolvents of symmetric operators with arbitrary defect numbers
Mathematical Notes of the Academy of Sciences of the USSR, 1976We establish a formula for generalized resolvents of a closed symmetric operator with arbitrary defect numbers. This formula resembles the Krein-Saakyan formula for the case of equal defect numbers.
Aleksandrov, E. L., Il'mushkin, G. M.
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On generalized resolvents of Hermitian operators in Krein spaces
Ukrainian Mathematical Journal, 1994See the review in Zbl 0838.47025.
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EXTENSIONS AND GENERALIZED RESOLVENTS OF A SYMMETRIC OPERATOR WHICH IS NOT DENSELY DEFINED
Mathematics of the USSR-Izvestiya, 1970We consider extensions of a closed symmetric operator whose domain is, in general, not dense in the given Hilbert space . In particular, we study self-adjoint extensions outside and the one-parameter families of operators () generated by them in which are dissipative for . The set of all generalized resolvents of the operator is characterized.
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Generalized Resolvents of a Class of Symmetric Operators in Krein Spaces
2007Let A be a closed symmetric operator of defect one in a Krein space K and assume that A possesses a self-adjoint extension in K which locally has the same spectral properties as a definitizable operator. We show that the Krein-Naimark formula establishes a bijective correspondence between the compressed resolvents of locally definitizable self-adjoint ...
Jussi Behrndt +2 more
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On a formula of the generalized resolvents of a nondensely defined Hermitian operator
Ukrainian Mathematical Journal, 1992The Weyl function and the prohibited lineal, corresponding to a given space of boundary values of a nondensely defined Hermitian operator, are introduced and investigated. The prohibited lineal is characterized in terms of the limiting values of the Weyl function. An analogue of M. G.
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