Invertibility and the Fredholm property of difference operators

DOI10.1007/BF02675622zbMath0979.47019MaRDI QIDQ5942055

Anatoly G. Baskakov

Publication date: 28 August 2001

Published in: Mathematical Notes (Search for Journal in Brave)

zbMATH Keywords

Fredholm propertyexponential dichotomydifference operatorinvertibilityevolution operatoruniform injectivity

Mathematics Subject Classification ID

(Semi-) Fredholm operators; index theories (47A53) General (adjoints, conjugates, products, inverses, domains, ranges, etc.) (47A05) Linear difference operators (47B39)

Related Items (15)

Linear differential operators and operator matrices of the second order ⋮ Bounded solutions of evolutionary equations. I ⋮ Nonlinear autonomous difference operators in the space of bounded sequences that are \(C^1\)-diffeomorphisms ⋮ Global bifurcation of homoclinic trajectories of discrete dynamical systems ⋮ Persistence and imperfection of nonautonomous bifurcation patterns ⋮ Fine structure of the dichotomy spectrum ⋮ Exponentially dichotomous difference equations with piecewise constant operator coefficients ⋮ Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations ⋮ Fredholm differential operators with unbounded coefficients ⋮ Invertibility Conditions for Second Order Difference Operators ⋮ Bounded solutions of evolutionary equations ⋮ Necessary and sufficient conditions for the invertibility of piecewise-autonomous difference operators in the space of bounded two-sided sequences ⋮ A note on the dichotomy spectrum ⋮ Bounded solutions of the nonlinear Lyapunov equation and homoclinic chaos ⋮ Bounded (on \(\mathbb{Z}\)) solutions of one difference equation

Cites Work

• Unnamed Item
• Algebras of difference and integral operators
• Geometric theory of semilinear parabolic equations
• Abstract harmonic analysis and asymptotic estimates of elements of inverse matrices
• Discrete operator convolutions and some of their applications
• Semigroups of difference operators in spectral analysis of linear differential operators
• On correct linear differential operators

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