Finite Section Method for Difference Equations
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A finite section method is developed for linear difference equations over an infinite time interval. A necessary and sufficient condition is given in order that the solutions of such equations may be obtained as limits of solutions of corresponding equations over a finite time interval. Both the time-variant and the time-invariant case are considered. For the time-invariant case the condition reduces to the requirement that two subspaces defined in terms of the equations should be complementary. The results obtained extend those derived earlier for linear ordinary differential equations.
KeywordsDifference Equation Bounded Sequence Finite Time Interval Spectral Projection Invertible Operator
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- Ben-Artzi, A., Gohberg, I., Kaashoek, M.A., Invertibility and dichotomy of singular difference equations, in: Topics in Operator Theory. Ernst D. Hellinger Memorial Volume (Eds. L. de Branges, I. Gohberg and J. Rovnyak), Birkhauser Verlag, Basel, OT 48 (1990), pp. 157–184.Google Scholar
- Böttcher, A., Infinite Matrices and Projection Methods, in: Lectures on Operator Theory and Its Applications (Ed. P. Lancaster), Amer. Math. Soc., Providence (RI), (1996), pp. 1–72.Google Scholar
- Gohberg, I., Feldman, I.A., Convolution Equations and Projection Methods for Their Solution,Amer. Math. Soc. Transl. of Math. Monographs 41, Providence (RI), (Russian Original: Nauka, Moscow, 1971), 1974.Google Scholar
- Gohberg, I., Kaashoek, M.A., Schagen, F. van, Finite section method for linear ordinary differential equations on the full line, submitted for publication (2000), 312–334.Google Scholar