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Positive Definite Sequence

المؤلف:  Widder, D. V.

المصدر:  The Laplace Transform. Princeton, NJ: Princeton University Press, 1941.

الجزء والصفحة:  ...

3-11-2020

939

Positive Definite Sequence

A sequence {mu_n}_(n=0)^infty" src="https://mathworld.wolfram.com/images/equations/PositiveDefiniteSequence/Inline1.gif" style="height:17px; width:43px" /> is positive definite if the moment of every nonnegative polynomial which is not identically zero is greater than zero (Widder 1941, p. 132). Here, the moment of a polynomial

with respect to the sequence {mu_n}_(n=0)^infty" src="https://mathworld.wolfram.com/images/equations/PositiveDefiniteSequence/Inline2.gif" style="height:17px; width:43px" /> is defined as

(Widder 1941, p. 102).

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REFERENCES:

Widder, D. V. The Laplace Transform. Princeton, NJ: Princeton University Press, 1941.