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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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Splitting Schemes for One Class of Operator Differential Equations
AbstractAt present, splitting schemes of various types are available for evolution equations of the first and second order in the case when the basic...
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Canonical Forms of an Operator
In this chapter, we study the structure of linear operators. In all that follows, V will be a finite dimensional vector space and...
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Operator splitting based dynamic iteration for linear differential-algebraic port-Hamiltonian systems
A dynamic iteration scheme for linear differential-algebraic port-Hamiltonian systems based on Lions–Mercier-type operator splitting methods is...
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Trotter-Kato Product Formulae: Operator-Norm Topology and Error Bounds
In this chapter, we present two fundamental results about the operator-norm optimal error bound estimates for convergence rate of the Trotter-Kato...
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Trace Formula for a Bounded Perturbation of the Laplace Operator on the Square
AbstractWe obtain the classical Gelfand–Levitan trace formula with subtraction of the first-order perturbation theory correction for the Laplace...
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Data-Driven Operator Theoretic Methods for Phase Space Learning and Analysis
This paper uses data-driven operator theoretic approaches to explore the global phase space of a dynamical system. We defined conditions for...
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Kähler manifolds and the curvature operator of the second kind
This article aims to investigate the curvature operator of the second kind on Kähler manifolds. The first result states that an m -dimensional Kähler...
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A generalized forward–backward splitting operator: degenerate analysis and applications
In this paper, we study the nonexpansive properties of a generalized forward–backward splitting (G-FBS) operator, particularly under the setting of...
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Operator Spectrum Transformation in Hartree–Fock and Kohn–Sham Equations
AbstractThe paper proposes a method for preliminary transformation of the spectrum of the equation operator both in the Hartree–Fock method and in...
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The Laplace Operator and the Geometry of Graphs
Graph Laplacians compare the value of a function at a vertex with the average of the values of its neighbors. Depending on the choices of scalar...
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Spectral theory of the multi-frequency quasi-periodic operator with a Gevrey type perturbation
In this paper we study the multi-frequency quasi-periodic operator with a Gevrey type perturbation. We first establish the large deviation theorem...
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Convergence of Some Difference Schemes of the Support Operator Method for Repeated Rotational Operations
AbstractAn approach for describing the metric properties of a difference mesh for discretizing repeated rotational operations of vector analysis as...
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Asymptotics of the eigenvalues of a two-term fourth-order operator with boundary conditions dependent on the spectral parameter
We consider a fourth-order ordinary differential operator with boundary conditions dependent on the spectral parameter. The potential is real-valued...
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Rokhlin-Type Properties of Group Actions on Operator Algebras
We give a survey of Rokhlin-type properties of group actions on operator algebras. Though we briefly review the classification of group actions on...