Tchakaloff’s theorem and $K$-integral polynomials in Banach spaces
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- by Damián Pinasco and Ignacio Zalduendo PDF
- Proc. Amer. Math. Soc. 145 (2017), 3395-3408 Request permission
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 $E$.References
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Additional Information
- 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
- MR Author ID: 186385
- Email: nacho@utdt.edu
- 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
- © Copyright 2017 American Mathematical Society
- 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
- MathSciNet review: 3652793