Abstract
Sufficient conditions are given in order that the solution of a linear ordinary differential equation on the full line is obtained as the limit of solutions of corresponding equations on finite intervals with boundary conditions or on half lines with initial conditions. Both the time-variant and the time-invariant case are considered, and in the latter case the sufficient conditions are also shown to be necessary. Included are applications to integral equations with semi-separable kernels.
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References
A. Böttcher, Infinite Matrices and Projection Methods, in “Lectures on Operator Theory and Its Applications”, Amer. Math. Soc., Providence (RI), 1996.
H. Bart, I. Gohberg, M.A. Kaashoek, Convolution equations and linear systemsIntegral Equations and Operator Theory, 5 (1982), 283–340.
W.A. Coppel, “Dichotomies in Stability Theory”, Lecture Notes in Mathematics, Springer-Verlag, Berlin, Heidelberg, New York, 1978.
I. Gohberg, I.A. Feldman, “Convolution Equations and Projection Methods for Their Solution”, Amer. Math. Soc. Transl. of Math. Monographs 41, Providence (RI), 1974 (Russian Original: Nauka, Moscow 1971).
I. Gohberg, M.A. Kaashoek, Time varying systems with boundary conditions and integral operators, I. The transfer operator and its propertiesIntegral Equations and Operator Theory7 (1984), 325–391.
I. Gohberg, M.A. Kaashoek, F. van Schagen, Non-compact integral operators with semi-separable kernels and their discrete analogues: inversion and Fredholm propertiesIntegral Equations and Operator Theory7 (1984), 642–703.
I. Gohberg, M.A. Kaashoek, F. van Schagen, Finite section method for linear ordinary differential equationsJournal of Differential Equationsto appear.
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© 2002 Springer Basel AG
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Gohberg, I., Kaashoek, M.A., van Schagen, F. (2002). Finite Section Method for Linear Ordinary Differential Equations on the Full Line. In: Alpay, D., Vinnikov, V., Gohberg, I. (eds) Interpolation Theory, Systems Theory and Related Topics. Operator Theory: Advances and Applications, vol 134. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8215-6_10
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DOI: https://doi.org/10.1007/978-3-0348-8215-6_10
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9477-7
Online ISBN: 978-3-0348-8215-6
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