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1
Content available On some extensions of the a-model
EN
The A-model for finite rank singular perturbations of class [formula], is considered from the perspective of boundary relations. Assuming further that the Hilbert spaces [formula] admit an orthogonal decomposition [formula], with the corresponding projections satisfying [formula], nontrivial extensions in the A-model are constructed for the symmetric restrictions in the subspaces.
EN
In this paper we propose an iterative algorithm based on the hybrid method in mathematical programming for approximating a common fixed point of an infinite family of left Bregman strongly nonexpansive mappings which also solves a finite system of equilibrium problems in a reflexive real Banach space.We further prove that our iterative sequence converges strongly to a common fixed point of an infinite family of left Bregman strongly nonexpansive mappings which is also a common solution to a finite system of equilibrium problems. Our result extends many recent and important results in the literature.
EN
We consider the operator T defined by (T f)(x)=(Sf)(x)+q(x)f(x), x ∈ Ω, where Ω ⊂ Rn is an unbounded domain, S is a positive definite selfadjoint operator defined on a domain Dom (S) ⊂ L2(Ω) and q(x) is a bounded complex measurable function with the property Im q(x) ∈ Lν(Ω) for a ν ∈ (1, ∞). We derive an estimate for the norm of the resolvent of T. In addition, we prove that T is invertible, and the inverse operator T-1 is a sum of a normal operator and a quasinilpotent one, having the same invariant subspaces. By the derived estimate, spectrum perturbations are investigated. Moreover, a representation for the resolvent of T by the multiplicative integral is established. As examples, we consider the Schrödinger operators on the positive half-line and orthant.
4
Content available remote On iterative convergence of resolvents of acceretive operators
EN
Weak and strong convergence of resolvents of accretive operators have been studied in this paper under different iteration schemes. In particular for an accretive operator A, the inclusion 0 Ax has been solved. Applying this result, we have found the solution of equation x + Bx = f where B is a Lipschitzian accretive operator.
5
Content available remote A nonstandard difference Sturm-Liouville operator
EN
After Nelson's Radically Elementary Probability Theory [1] a natural question arises: whether a hyperfinite-dimensional space is sufficiently rich to be used for the same goal as an infinite-dimensional one. Here a hyperfinite 3-diagonal matrix is investigated, which spectral properties are simular to the Naimarks's singular nonselfadjoint Sturm-Liouville differential operator on semi-axis [2, 3].
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