Abstract
Let T be a tridiagonal operator on which has strict row and column dominant property except for some finite number of rows and columns. This matrix is shown to be invertible under certain conditions. This result is also extended to double infinite tridiagonal matrices. Further, a general theorem is proved for solving an operator equation using its finite-dimensional truncations, where T is a double infinite tridiagonal operator. Finally, it is also shown that these results can be applied in order to obtain a stable set of sampling for a shift-invariant space.
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Acknowledgements
We thank the referee for meticulously reading the manuscript and giving us several valuable suggestions in improving the initial version of the manuscript. We also thank Prof. S. H. Kulkarni and Y .V. S. S. Sanyasiraju for some fruitful discussions and their useful suggestions.
Notes
No potential conflict of interest was reported by the authors.