منابع مشابه
Total positivity of a Cauchy kernel
We study the total positivity of the kernel 1/(x+2 cos(πα)xy+y). The case of infinite order is characterized by an application of Schoenberg’s theorem. We then give necessary conditions for the cases of any given finite order with the help of Chebyshev polynomials of the second kind. Sufficient conditions for the finite order cases are also obtained, thanks to Propp’s formula for the Izergin-Ko...
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متن کاملTotal positivity of Riordan arrays
An infinite matrix is called totally positive if its minors of all orders are nonnegative. A nonnegative sequence (an)n≥0 is called log-convex (logconcave, resp.) if aiaj+1 ≥ ai+1aj ( aiaj+1 ≤ ai+1aj , resp.) for 0 ≤ i < j . The object of this talk is to study various positivity properties of Riordan arrays, including the total positivity of such a matrix, the log-convexity of the 0th column an...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2014
ISSN: 0021-9045
DOI: 10.1016/j.jat.2014.05.014