A sufficient condition for strict total positivity of a matrix

Linear and Multilinear Algebra

Volumn 45, Issue 1, 1998, Pages 19-34

  Craven, Thomas ^a   Csordas, George ^a  

^a UNIVERSITY OF HAWAII   (United States)

Author keywords

Hankel matrix; Increasing sequence; Moment; Totally positive matrix

Indexed keywords

EID: 0009106065     PISSN: 03081087     EISSN: None     Source Type: Journal    
DOI: 10.1080/03081089808818575     Document Type: Article

References (15)

1. Ando, T. (1987). Totally positive matrices, Linear Algebra Appl., 90, 165-219.
2. Aissen, M., Schoenberg, I. J. and Whitney, A. M. (1952). On generating functions of totally positive sequences I, J. Anal. Math., 2, 93-103.
3. Brenti, F. (1989). Log-Concave and Pólya Frequency Sequences in Combinatorics, Memoirs of the Amer. Math. Soc., 81(413), Providence, RI.
4. Craven, T. and Csordas, G. (1995). Complex zero decreasing sequences, Methods Appl. Anal., 2, 420-441.
5. Edrei, A. (1952). On the generating functions of totally positive sequences II, J. Anal. Math., 2, 104-109.
6. Edrei, A. (1953). Proof of conjecture of Schoenberg on the generating function of a totally positive sequence, Canad. J. Math., 5, 86-94.
7. Edrei, A. (1953). On the generating function of a doubly infinite totally positive sequence, Trans. Amer. Math. Soc., 74, 367-383.
8. Gantmacher, F. R. (1959). The Theory of Matrices, Vols. 1 and 2, Chelsea Publishing Co., New York.
9. Gasca, M. and Peña, J. M. (1992). On the characterization of totally positive matrices. Approximation Theory, Spline Functions and Applications (Maratea, 1991), pp. 357-364, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Vol. 356, Kluwer Acad. Publ., Dordrecht.
10. Gasca, M. and Peña, J. M. (1992). Total positively and Neville elimination, Linear Algebra Appl., 165, 25-44.
11. Gasca, M. and Peña, J. M. (1996). On factorizations of totally positive matrices, Total Positivity and its Applications (Jaca, 1994), pp. 109-130, Kluwer Acad. Publ., Dordrecht.
12. Karlin, S. (1968). Total Positivity, Vol. 1, Stanford Univ. Press, Stanford, Calif.
13. Polya, G. and Szegö, G. (1976). Problems and Theorems in Analysis, Vols. I and II, Springer-Verlag, New York.
14. Widder, D. V. (1941). The Laplace Transform, Princeton Univ. Press, Princeton.
15. Schoenberg, I. J. (1951). On Pólya frequency functions I. The totally positive functions and their Laplace transforms, J. Anal. Math., 1, 331-374.