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Structure of invertible (bi)infinite totally positive matrices. (English) Zbl 0504.15014


MSC:

15B48 Positive matrices and their generalizations; cones of matrices
47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
46A45 Sequence spaces (including Köthe sequence spaces)
15A23 Factorization of matrices
Full Text: DOI

References:

[1] de Boor, C., Odd-degree spline interpolation at a biinfinite knot sequence, (Schaback, R.; Scherer, K., Approximation Theory, Bonn 1976. Approximation Theory, Bonn 1976, Lecture Notes Math., 556 (1976), Springer: Springer Heidelberg), 30-53 · Zbl 0337.41004
[2] de Boor, C., What is the main diagonal of a biinfinite band matrix?, (DeVore, R.; Scherer, K., Quantitative Approximation (1980), Academic), 11-23 · Zbl 0457.41014
[3] de Boor, C., The inverse of a totally positive biinfinite band matrix, MRC TSR 2155. MRC TSR 2155, Trans. Amer. Math. Soc. (1980), to appear
[4] de Boor, C.; Friedland, S.; Pinkus, A., Inverses of infinite sign regular matrices, Trans. Amer. Math. Soc. (1980), to appear · Zbl 0502.47015
[5] Cavaretta, A.; Dahmen, W.; Micchelli, C. A.; Smith, P., On the solvability of certain systems of linear difference equations, SIAM J. Math. Anal., 12, 833-841 (1981) · Zbl 0482.15011
[6] Cavaretta, A.; Dahmen, W.; Micchelli, C. A.; Smith, P., A factorization theorem for band matrices, Linear Algebra Appl., 39, 229-245 (1980), (1981) · Zbl 0467.15005
[7] Demko, S., Inverses of band matrices and local convergence of spline projectors, SIAM J. Numer. Anal., 14, 616-619 (1977) · Zbl 0367.65024
[8] Karlin, S., Total Positivity (1968), Stanford U.P · Zbl 0219.47030
[9] Micchelli, C. A., Infinite spline interpolation, (Meinardus, G., Approximation in Theorie und Praxis. Ein Symposiumsbericht (1979), Bibliographisches Institut: Bibliographisches Institut Mannheim), 209-238 · Zbl 0435.41006
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