Results 1 to 10 of about 3,267 (95)
A Generalization of a Classic Theorem in the Perturbation Theory for Linear Operators
Journal of Mathematical Analysis and Applications, 1999 Let \(T\) be a bounded linear operator of a Banach space \(X\) into another \(Y\) such that the null space \(N(T)\) is a complementary subspace of \(X\) and the range \(R(T)\) a complementary subspace of \(Y\). This note considers the equation \(Tx= y\) for given \(y\) and its perturbed one \((T+\delta T)\widetilde x= y+\delta y\), to estimate the norm
Ding, Jiu, Huang, L.J.
openaire +3 more sources
Linear Algebra and its Applications, 2012 The authors develop a quantitative perturbation theory for the approximation of stability spectra of sequences of infinite dimensional operators based on an infinite dimensional \(QR\) technique for determining Lyapunov exponents and Sacker-Sell spectrum. The results apply also in the case of stable but not necessarily distinct Lyapunov exponents.
Badawy, M., Van Vleck, E.
openaire +3 more sources
Multiparameter perturbation theory of matrices and linear operators [PDF]
Transactions of the American Mathematical Society, 2020 We show that a normal matrix A A with coefficients in
Parusiński, Adam, Rond, Guillaume
openaire +3 more sources
Spectral theory for structured perturbations of linear operators [PDF]
Journal of Spectral Theory, 2018 We characterize the spectrum (and its parts) of operators which can be represented as " G=A+BC“ for a "simpler" operator A and a structured perturbation
ENGEL, KLAUS JOCHEN OTTO, Adler, Martin
openaire +3 more sources
The perturbation theory for linear operators of discrete type [PDF]
Pacific Journal of Mathematics, 1983 A perturbation result for unbounded operators of discrete type [\textit{N. Dunford} and \textit{J. Schwartz}, Linear Operators, part III (1971; Zbl 0243.47001): Spectral Operators, XIX, 2, Theorem 7] is derived using the notion of unconditional basis instead of assuming weak completeness of the underlying Banach space.
openaire +2 more sources
Effective perturbation theory for linear operators
Journal of Operator Theory, 2017 We propose a new approach to the spectral theory of perturbed linear operators , in the case of a simple isolated eigenvalue. We obtain two kind of results: ''radius bounds'' which ensure perturbation theory applies for perturbations up to an explicit size, and ''regularity bounds'' which control the variations of eigendata to any order.
openaire +4 more sources
Perturbation Theory of Polynomials and Linear Operators
66 pages. The numbering of equations was changed, and a few more modifications were made. This final version will appear as a chapter in the book series "Handbook of Geometry and Topology of Singularities", Vol ...
Parusiński, Adam, Rainer, Armin
openaire +2 more sources
Constructing Linear Operators Using Classical Perturbation Theory
Journal of Guidance, Control, and DynamicsThis work introduces a methodology for generating linear operators that approximately represent nonlinear systems of perturbed ordinary differential equations. This is done through the application of classical perturbation theory via the Lindstedt–Poincaré expansion, followed by an extension of the space of configuration that guarantees the linear ...
Miguel Avillez, David Arnas
openaire +2 more sources
Acta Physica Sinica, 1989 The interaction potential with the form as V(x)= x2+λx2/(1+gx2) where g >0, appears in several areas of laser theory, quantum field theory, atom and nuclear physics. One could consider that the solution of the eigenequation either by the classical Rayleigh-Schr?dinger perturbation scheme or by the perturbed ladder operators scheme. Nevertheless, the
openaire +1 more source
On the perturbation theory of closed linear operators.
Journal of the Mathematical Society of Japan, 1952 openaire +3 more sources