Wyniki wyszukiwania - Biblioteka Nauki

1

Resolvent of nonautonomous linear delay functional differential equations

100%

Blot J. , Koné M. I.

Nonautonomous Dynamical Systems

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2015

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tom 2

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nr 1

EN

The aim of this paper is to give a complete proof of the formula for the resolvent of a nonautonomous linear delay functional differential equations given in the book of Hale and Verduyn Lunel [9] under the assumption alone of the continuity of the right-hand side with respect to the time,when the notion of solution is a differentiable function at each point, which satisfies the equation at each point, and when the initial value is a continuous function.

2

A note on Hausdorff convergence of pseudospectra

80%

Lindner M. , Schmeckpeper D.

Opuscula Mathematica

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2023

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tom Vol. 43, no. 1

101--108

EN

For a bounded linear operator on a Banach space, we study approximation of the spectrum and pseudospectra in the Hausdorff distance. We give sufficient and necessary conditions in terms of pointwise convergence of appropriate spectral quantities.

3

On iterative convergence of resolvents of acceretive operators

60%

Khan S. H.

Demonstratio Mathematica

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2004

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tom Vol. 37, nr 2

407--417

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.

4

An estimate for the resolvent of a non-selfadjoint differential operator on an unbounded domain

60%

Gil` M. I.

Journal of Applied Analysis

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2013

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tom Vol. 19, nr 2

231--246

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.

5

A note on convergence of semigroups

60%

Bobrowski A.

Annales Polonici Mathematici

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1998

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tom 69

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nr 2

107-127

EN

Convergence of semigroups which do not converge in the Trotter-Kato-Neveu sense is considered.

6

On some extensions of the a-model

41%

Jursenas R.

Opuscula Mathematica

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2020

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tom Vol. 40, no. 5

569--597

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.

7

Approximation of common fixed points of left Bregman strongly nonexpansive mappings and solutions of equilibrium problems

41%

Shehu Y. , Ogbuisi F. U.

Journal of Applied Analysis

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2015

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tom Vol. 21, nr 2

63--77

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.

8

A nonstandard difference Sturm-Liouville operator

36%

Javorskij J. , Ljance V.

Bulletin of the Polish Academy of Sciences. Mathematics

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1998

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tom Vol. 46, no 3

285-290

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].

9

Resolvent Flows for Convex Functionals and p-Harmonic Maps

36%

Kuwae K.

Analysis and Geometry in Metric Spaces

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2015

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tom 3

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nr 1

EN

We prove the unique existence of the (non-linear) resolvent associated to a coercive proper lower semicontinuous function satisfying a weak notion of p-uniform λ-convexity on a complete metric space, and establish the existence of the minimizer of such functions as the large time limit of the resolvents, which generalizing pioneering work by Jost for convex functionals on complete CAT(0)-spaces. The results can be applied to Lp-Wasserstein space over complete p-uniformly convex spaces. As an application, we solve an initial boundary value problem for p-harmonic maps into CAT(0)-spaces in terms of Cheeger type p-Sobolev spaces.