Bibliography
M. Aissen, I. J. Schoenberg and A. Whitney, On the generating function of totally positive sequences I,Jour. d’Analyse Math., 2 (1852), pp. 93–103.
A. Edrei, On the generating functions of totally positive sequences, II,Jour. d’Analyse Math., 2 (1952), pp. 104–109.
A. Edrei, On the generating function of a doubly infinite totally positive sequence,Trans. Amer. Math. Soc., 74 (1953), 367–383.
A. Erdélyi, et al., Higher Transcendental Functions, New York, 1953.
I. I. Hirschman, Jr. Harmonic analysis and ultraspherical polynomials, Symposium on Harmonic Analysis and Related Integral Transforms, Cornell Univ. (1956).
I. I. Hirschman, Jr., Variation diminishing Hankel transforms and Variation diminishing transformations and ultraspherical polynomials,Jour. d’Analyse Math., 8 (1960–1961), pp. 307–336 and 337–360.
I. I. Hirschman, Jr., and D. V. Widder, The Convolution Transform, Princeton, 1955.
G. Pólya and G. Szegö, Aufgaben und LehrsÄtze aus der Analysis, Berlin, 1925.
I. J. Schoenberg, On Pólya frequency functions I,Jour. d’Analyse Math., 1 (1951), pp. 331–374.
I. J. Schoenberg, On Pólya frequency functions, II,Acta Scientiarum Mathe.- matkarum Szeged, 12 (1950).
I. J. Schoenberg, Some analytical aspects of the problem of smoothing, Courant Anniversary Volume, New York, 1948, pp. 351–370.
G. Szegö, Orthogonal Polynomials, New York, 1939.
A. Whitney, A reduction theorem for totally positive matrices.Jour. d’Analyse Math., 2 (1952), pp. 88–92.
Author information
Authors and Affiliations
Additional information
Research supported in part by the Air Force Office of Scientific Research and Development Command under contract No. AF 49 (638)-218.
This Paper was submitted to the Canadian Journal of Mathematics on July 8, 1960 and was accepted for publication. The author wishes to thank the editors of the Canadian Journal for their kindness in releasing this paper so that it could be published in the present journal, together with two earlier papers on the same subject.
Rights and permissions
About this article
Cite this article
Hirschman, I.I. Variation diminishing transformations and orthogonal polynomials. J. Anal. Math. 9, 177–193 (1961). https://doi.org/10.1007/BF02795343
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02795343