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Resolvent of a Schrödinger Operator on a Model Graph with Small Loops
We consider a Schrödinger operator on a model graph with small loops assuming the violation of the typical nonresonance condition which guarantees...
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Analysis of Abstract Partial Impulsive Integro-Differential System with Delay via Integrated Resolvent Operator
In this manuscript, we employ integrated resolvent operator to derive the variation of constants formula for the solution of the impulsive...
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Operator-norm resolvent estimates for thin elastic periodically heterogeneous rods in moderate contrast
We provide resolvent asymptotics as well as various operator-norm estimates for the system of linear partial differential equations describing thin...
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A note on the compactness of the resolvent of the age-diffusion operator
The generator of the semigroup associated with linear age-structured population models including spatial diffusion is shown to have compact resolvent.
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On the Structure of the Spectrum and the Resolvent Set of a Toeplitz Operator in a Countably Normed Space of Smooth Functions
AbstractIn the countably normed space of smooth functions on the unit circle, we consider a Toeplitz operator with a smooth symbol. Questions...
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One Condition for Discreteness of the Spectrum and Compactness of the Resolvent of a Nonsectorial Sturm–Liouville Operator on a Semiaxis
AbstractThe spectral properties of the Sturm–Liouville operator on a semiaxis in the case of a complex-valued potential with a range exceeding the...
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Resolvent of the parallel composition and the proximity operator of the infimal postcomposition
In this paper we provide the resolvent computation of the parallel composition of a maximally monotone operator by a linear operator under mild...
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Resolvent and Proximal Compositions
We introduce the resolvent composition, a monotonicity-preserving operation between a linear operator and a set-valued operator, as well as the...
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Frugal and decentralised resolvent splittings defined by nonexpansive operators
Frugal resolvent splittings are a class of fixed point algorithms for finding a zero in the sum of the sum of finitely many set-valued monotone...
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On the Metric Resolvent: Nonexpansiveness, Convergence Rates and Applications
In this paper, we study the nonexpansive properties of metric resolvent and present the convergence analysis for the associated fixed-point...
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Browder S-Resolvent Equation in Quaternionic Setting
This paper is devoted to the study of the S -eigenvalue of finite type of a bounded right quaternionic linear operator acting in a right quaternionic...
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Approximation semigroups for resolvent maps
In this paper, we extend the results for approximation semigroups for general resolvent maps including various resolvents of maps on a general convex...
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Resolvent Asymptotics Near a Two-Cluster Threshold
This chapter is devoted to the asymptotics of the resolvent near an arbitrary two-cluster threshold...
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Representations of abstract resolvent families on time scales via Laplace Transform
In this work we introduce a general formulation of resolvent family, also named resolvent operator, to describe explicit formulas for the solutions...
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Asymptotic Stability of Riemann–Liouville Fractional Resolvent Families
In this paper, we investigate the asymptotic stability of Riemann–Liouville fractional resolvent families (R–L resolvent families) on Banach spaces...
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The Cayley–Hamilton Theorem and Resolvent Representation
AbstractFor the Frobenius matrix accompanying an algebraic (differential) equation in a complex Banach algebra, the Cayley–Hamilton theorem is...
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Discussing Semigroup Bounds with Resolvent Estimates
The purpose of this paper is to revisit the proof of the Gearhardt–Prüss–Huang–Greiner theorem for a semigroup S ( t ), following the general idea of...
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Resolvent Algebra in Fock-Bargmann Representation
The resolvent algebra \(\mathfrak {R}\left( X, \sigma \right) \)...