Tchakaloff's theorem and K-integral polynomials in Banach spaces (English)

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Tchakaloff's theorem gives a quadrature formula for polynomials of a given degree with respect to a compactly supported positive measure which is absolutely continuous with respect to Lebesgue measure. We study the validity of two possible analogues of Tchakaloff's theorem in an infinite-dimensional Banach space E: a weak form valid when E has a Schauder basis, and a stronger form requiring conditions on the support of the measure as well as on the space E.

Table of contents – Volume 145, Issue 8

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