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Tchakaloff's theorem and $ K$-integral polynomials in Banach spaces


Authors: Damián Pinasco and Ignacio Zalduendo
Journal: Proc. Amer. Math. Soc. 145 (2017), 3395-3408
MSC (2010): Primary 46E50; Secondary 28C20, 46G12, 46G20
DOI: https://doi.org/10.1090/proc/13520
Published electronically: January 25, 2017
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Abstract: 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$.


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Damián Pinasco
Affiliation: Departamento de Matemática, Universidad Torcuato Di Tella, Av. Figueroa Alcorta 7350 (C1428BCW), Buenos Aires, Argentina – and – CONICET
Email: dpinasco@utdt.edu

Ignacio Zalduendo
Affiliation: Departamento de Matemática, Universidad Torcuato Di Tella, Av. Figueroa Alcorta 7350 (C1428BCW), Buenos Aires, Argentina – and – CONICET
Email: nacho@utdt.edu

DOI: https://doi.org/10.1090/proc/13520
Keywords: Polynomials on Banach spaces, integral polynomial, nuclear polynomial, Tchakaloff's theorem.
Received by editor(s): October 29, 2015
Received by editor(s) in revised form: July 4, 2016, and August 31, 2016
Published electronically: January 25, 2017
Additional Notes: The authors were partially supported by CONICET (PIP 11220090100624).
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2017 American Mathematical Society

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