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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Embeddings of Müntz spaces: The Hilbertian case
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by S. Waleed Noor and Dan Timotin PDF
Proc. Amer. Math. Soc. 141 (2013), 2009-2023 Request permission

Abstract:

Given a strictly increasing sequence $\Lambda =(\lambda _n)$ of nonnegative real numbers, with $\sum _{n=1}^\infty \frac {1}{\lambda _n}<\infty$, the Müntz spaces $M_\Lambda ^p$ are defined as the closure in $L^p([0,1])$ of the monomials $x^{\lambda _n}$. We discuss properties of the embedding $M_\Lambda ^p\subset L^p(\mu )$, where $\mu$ is a finite positive Borel measure on the interval $[0,1]$. Most of the results are obtained for the Hilbertian case $p=2$, in which we give conditions for the embedding to be bounded, compact, or to belong to the Schatten–von Neumann ideals.
References
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Additional Information
  • S. Waleed Noor
  • Affiliation: Abdus Salam School of Mathematical Sciences, New Muslim Town, Lahore, 54600, Pakistan
  • Email: waleed_math@hotmail.com
  • Dan Timotin
  • Affiliation: Institute of Mathematics of the Romanian Academy, Calea Griviţei 21, Bucharest, Romania
  • Email: Dan.Timotin@imar.ro
  • Received by editor(s): September 18, 2011
  • Published electronically: December 18, 2012
  • Communicated by: Richard Rochberg
  • © Copyright 2012 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 141 (2013), 2009-2023
  • MSC (2010): Primary 46E15, 46E20, 46E35
  • DOI: https://doi.org/10.1090/S0002-9939-2012-11681-8
  • MathSciNet review: 3034427