Generalized Eigenvalues of Nonsquare Pencils with Structure

2008 ◽  
Vol 30 (1) ◽  
pp. 41-55 ◽  
Author(s):  
Pablo Lecumberri ◽  
Marisol Gómez ◽  
Alfonso Carlosena
Keyword(s):  
Generalized Eigenvalues

scholarly journals Generalized principal eigenvalues of convex nonlinear elliptic operators in ℝN

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Anup Biswas ◽  
Prasun Roychowdhury
Keyword(s):  
Eigenvalue Problem ◽  
Principal Eigenvalue ◽  
Unbounded Domains ◽  
Elliptic Operators ◽  
Maximum Principles ◽  
Generalized Eigenvalues ◽  
Nonlinear Elliptic ◽  
Generalized Eigenvalue ◽  
General Convex ◽  
Appl Math

AbstractWe study the generalized eigenvalue problem in {\mathbb{R}^{N}} for a general convex nonlinear elliptic operator which is locally elliptic and positively 1-homogeneous. Generalizing [H. Berestycki and L. Rossi, Generalizations and properties of the principal eigenvalue of elliptic operators in unbounded domains, Comm. Pure Appl. Math. 68 2015, 6, 1014–1065], we consider three different notions of generalized eigenvalues and compare them. We also discuss the maximum principles and uniqueness of principal eigenfunctions.

A neurodynamic approach to compute the generalized eigenvalues of symmetric positive matrix pair

2019 ◽  
Vol 359 ◽  
pp. 420-426
Author(s):  
Jiqiang Feng ◽  
Su Yan ◽  
Sitian Qin ◽  
Wen Han
Keyword(s):  
Positive Matrix ◽  
Generalized Eigenvalues ◽  
Matrix Pair

scholarly journals GENERALIZED EIGENVECTORS FOR RESONANCES IN THE FRIEDRICHS MODEL AND THEIR ASSOCIATED GAMOV VECTORS

2006 ◽  
Vol 18 (01) ◽  
pp. 61-78 ◽  
Author(s):  
HELLMUT BAUMGÄRTEL
Keyword(s):  
Hardy Space ◽  
Half Plane ◽  
Lower Half Plane ◽  
Linear Forms ◽  
Generalized Eigenvalues ◽  
Dirac Type ◽  
Generalized Eigenvectors ◽  
Upper Half Plane ◽  
Friedrichs Model ◽  
Generalized Eigenvector

A Gelfand triplet for the Hamiltonian H of the Friedrichs model on ℝ with multiplicity space [Formula: see text], [Formula: see text], is constructed such that exactly the resonances (poles of the inverse of the Livšic-matrix) are (generalized) eigenvalues of H. The corresponding eigen(anti)linear forms are calculated explicitly. Using the wave matrices for the wave (Möller) operators the corresponding eigen(anti)linear forms on the Schwartz space [Formula: see text] for the unperturbed Hamiltonian H0 are also calculated. It turns out that they are of pure Dirac type and can be characterized by their corresponding Gamov vector λ → k/(ζ0 - λ)-1, ζ0 resonance, [Formula: see text], which is uniquely determined by restriction of [Formula: see text] to [Formula: see text], where [Formula: see text] denotes the Hardy space of the upper half-plane. Simultaneously this restriction yields a truncation of the generalized evolution to the well-known decay semigroup for t ≥ 0 of the Toeplitz type on [Formula: see text]. That is: Exactly those pre-Gamov vectors λ → k/(ζ - λ)-1, ζ from the lower half-plane, [Formula: see text], have an extension to a generalized eigenvector of H if ζ is a resonance and if k is from that subspace of [Formula: see text] which is uniquely determined by its corresponding Dirac type antilinear form.

Localization of generalized eigenvalues by Cartesian ovals

2011 ◽  
Vol 19 (4) ◽  
pp. 728-741 ◽  
Author(s):  
V. Kostić ◽  
R. S. Varga ◽  
L. Cvetković
Keyword(s):  
Generalized Eigenvalues ◽  
Cartesian Ovals
Sign in / Sign up

Export Citation Format

Share Document