Enclosure of the numerical range of a class of non-selfadjoint rational operator functions

DOI10.1007/s00020-017-2378-6OpenAlexW2509216222WikidataQ59611331 ScholiaQ59611331MaRDI QIDQ1676930

Axel Torshage, Christian Engström

Publication date: 10 November 2017

Published in: Integral Equations and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1604.07586

zbMATH Keywords

numerical rangepseudospectraresolvent estimatenon-linear spectral problem

Mathematics Subject Classification ID

Numerical range, numerical radius (47A12) Functions whose values are linear operators (operator- and matrix-valued functions, etc., including analytic and meromorphic ones) (47A56) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10)

Related Items (8)

Pseudo numerical ranges and spectral enclosures ⋮ Spectra of Gurtin-Pipkin type of integro-differential equations and applications to waves in graded viscoelastic structures ⋮ Enclosure of the numerical range and resolvent estimates of non-selfadjoint operator functions ⋮ \(\varepsilon\)-numerical range of operator polynomial ⋮ On equivalence and linearization of operator matrix functions with unbounded entries ⋮ Numerical solution of distributed-order time-fractional diffusion-wave equations using Laplace transforms ⋮ Spectral properties of a class of operator functions with applications to the Moore-Gibson-Thompson equation with memory ⋮ Accumulation of complex eigenvalues of a class of analytic operator functions

Uses Software

• Eigtool

Cites Work

• Rational eigenvalue problems and applications to photonic crystals
• An elliptic boundary value problem depending nonlinearly upon the eigenvalue parameter
• Point equation of the boundary of the numerical range of a matrix polynomial
• Perturbation theory for linear operators.
• Variational principles for eigenvalues of self-adjoint operator functions
• Linearization techniques for band structure calculations in absorbing photonic crystals
• Numerical Range of Matrix Polynomials
• On the Numerical Range of Rational Matrix Functions
• A spectral theory for a \(\lambda\)-rational Sturm-Liouville problem
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