Search Results - (Generalized) eigenfunction expansions of linear operators

The Generalized Operator Based Prony Method by Stampfer, Kilian, Plonka, Gerlind

“…The generalized Prony method is a reconstruction technique for a large variety of sparse signal models that can be represented as sparse expansions into eigenfunctions of a linear operator…”
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Spectrum of the Koopman Operator, Spectral Expansions in Functional Spaces, and State-Space Geometry by Mezić, Igor

“… Using the Kato decomposition, we develop a spectral expansion for general linear autonomous dynamical systems with analytic observables and define the notion of generalized eigenfunctions…”
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On Eigenfunction Expansion of Solutions to the Hamilton Equations by Komech, A., Kopylova, E.

“… Our main result is an application to the eigenfunction expansion for the linearized relativistic Ginzburg–Landau equation…”
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Time-dependent linear water-wave scattering in two dimensions by a generalized eigenfunction expansion by MEYLAN, MICHAEL H.

“… We show how the problem with arbitrary initial conditions can be found from the single-frequency solutions using a generalized eigenfunction expansion, required because the operator has a continuous spectrum…”
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Mathematical Analysis of Deterministic and Stochastic Problems in Complex Media Electromagnetics by Roach, G. F, Stratis, Ioannis G, Yannacopoulos, Athanassios N

“…Electromagnetic complex media are artificial materials that affect the propagation of electromagnetic waves in surprising ways not usually seen in nature…”
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On Titchmarsh–Weyl Functions and Eigenfunction Expansions of First-Order Symmetric Systems by Albeverio, Sergio, Malamud, Mark, Mogilevskii, Vadim

“…We study general (not necessarily Hamiltonian) first-order symmetric system J y ′( t )− B ( t ) y ( t ) = Δ( t ) f ( t ) on an interval I = [ a , b ) with the…”
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A GENERAL SPECTRAL APPROACH TO THE TIME-DOMAIN EVOLUTION OF LINEAR WATER WAVES IMPACTING ON A VERTICAL ELASTIC PLATE by PETER, MALTE A., MEYLAN, MICHAEL H.

“… The problem is solved using a generalized eigenfunction expansion from the solutions for single frequencies, and we begin with a novel solution of the single-frequency problem…”
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On characteristic matrices and eigenfunction expansions of two singular point symmetric systems by Mogilevskii, Vadim

“… We prove the Titchmarsh type formula for the characteristic matrix Ω(λ) of the self‐adjoint linear relation in LΔ2…”
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Eigenfunction expansions in L 2 spaces for boundary value problems on time-scales by Davidson, Fordyce A., Rynne, Bryan P.

“…Let T ⊂ R be a bounded time-scale, with a = inf T , b = sup T . We consider the weighted, linear, eigenvalue problem − ( p u Δ ) Δ ( t ) + q ( t ) u σ ( t ) = λ…”
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Theory of Characteristic Modes for Nonsymmetric Surface Integral Operators by Yla-Oijala, Pasi, Wallen, Henrik

“…) operators, the eigenvectors are not orthogonal with respect to the weighted inner product defined with the weighting operator of the generalized eigenvalue equation…”
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The principle of general localization on unit sphere by Ahmedov, Anvarjon

“… . The properties Jacobi polynomials are used in estimating the maximal operators of spectral expansions in L 2 ( S N…”
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Eigenvalue Expansion of Nonsymmetric Linear Compact Operators in Hilbert Space by KOHAUPT, Ludwig

“…For a symmetric linear compact resp. symmetric densely defined linear operator with compact inverse, expansion theorems in series of eigenvectors are known…”
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Modifications of Prony's Method for the Recovery and Sparse Approximation of Generalized Exponential Sums by Keller, Ingeborg, Plonka, Gerlind

“…In this survey we describe some modifications of Prony's method. In particular, we consider the recovery of general expansions into eigenfunctions of linear…”
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Analysis of the method of generalized separation of variables in the problem of light scattering by small axisymmetric particles by Farafonov, V. G., Ustimov, V. I.

“… of variables method (GSVM). In this case, electric-field strengths are gradients of scalar potentials, which are represented as expansions in term of eigenfunctions of the Laplace operator in the spherical coordinate system…”
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Pseudo-Hermitian Reduction of a Generalized Heisenberg Ferromagnet Equation. I. Auxiliary System and Fundamental Properties by Yanovski, A. B., Valchev, T. I.

“… Using the concept of gauge equivalence, we construct expansions over the eigenfunctions of recursion operators…”
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The Generalized Operator Based Prony Method by Stampfer, Kilian, Plonka, Gerlind

“…The generalized Prony method introduced by Peter & Plonka (2013) is a reconstruction technique for a large variety of sparse signal models that can be represented as sparse expansions into eigenfunctions of a linear operator…”
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On relaxation processes in a completely ionized plasma by Alexander I. Sokolovsky, Sergey A. Sokolovsky, Oleh A. Hrinishyn

“… The plasma is considered in a generalized Lorentz model which contrary to standard one assumes that ions form an equilibrium system…”
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Limiting Absorption Principles and Linear Inviscid Damping in the Euler–Boussinesq System in the Periodic Channel by Coti Zelati, Michele, Nualart, Marc

“… of the generalized eigenfunction near the critical layer. As a by-product of our analysis, we provide a precise description of the spectrum of the linearized operator, which, for sufficiently large Richardson number, consists of an essential spectrum (as expected according to classical hydrodynamic problems) as well as discrete neutral eigenvalues (giving rise to oscillatory modes) accumulating towards the endpoints of the essential spectrum…”
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Spectrum of the Koopman Operator, Spectral Expansions in Functional Spaces, and State Space Geometry by Mezic, Igor

“… Using the Kato Decomposition we develop a spectral expansion for general linear autonomous dynamical systems with analytic observables, and define the notion of generalized eigenfunctions…”
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EIGENFUNCTION EXPANSIONS FOR PROBLEMS IN ELASTODYNAMICS (LINEAR) by HERCZYNSKI, ANDRZEJ

“… (Pochhammer-Chree modes). The orthogonality condition is obtained from the consideration of the generalized Wronskian, involving the eigenfunctions of the original and the dual space…”
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