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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Embeddings of Müntz spaces: The Hilbertian case


Authors: S. Waleed Noor and Dan Timotin
Journal: Proc. Amer. Math. Soc. 141 (2013), 2009-2023
MSC (2010): Primary 46E15, 46E20, 46E35
Published electronically: December 18, 2012
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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 [Enhancements On Off] (What's this?)

  • 1. I. Al Alam. Géometrie des espaces de Müntz et opérateurs de composition $ \grave {a}$ poids. PhD thesis, Université Lille 1, 2008.
  • 2. I. Al Alam. Essential norms of weighted composition operators on Müntz spaces, J. Math. Anal. Appl., 358(2), 2009. MR 2532505 (2010f:47046)
  • 3. J. Bergh and J. Löfström. Interpolation Spaces: An Introduction. Springer-Verlag, New York, 1976. MR 0482275 (58:2349)
  • 4. P. Borwein and T. Erdelyi. Polynomials and Polynomial Inequalities, volume 161 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1995. MR 1367960 (97e:41001)
  • 5. Th. J. Bromwich. An Introduction to the Theory of Infinite Series. Macmillan, London, 1908.
  • 6. I. Chalendar, E. Fricain, and Dan Timotin. Embedding theorems for Müntz spaces, Ann. Inst. Fourier (Grenoble), 61 (2011), 2291-2311. MR 2976312
  • 7. Ole Christensen. An Introduction to Frames and Riesz Bases, Applied and Numerical Harmonic Analysis. Birkhäuser, Boston, 2003. MR 1946982 (2003k:42001)
  • 8. J. Diestel, H. Jarchow, and A. Tonge. Absolutely Summing Operators, volume 43 of Cambridge Studies in Advanced Mathematics. Cambridge University Press, New York, 1995. MR 1342297 (96i:46001)
  • 9. V.I. Gurariy and W. Lusky. Geometry of Müntz Spaces and Related Questions, volume 1870 of Lecture Notes in Mathematics. Springer-Verlag, Berlin, 2005. MR 2190706 (2007g:46027)
  • 10. Charles A. McCarthy. $ c_p$, Israel Journal of Mathematics, 5 (1967), 249-271. MR 0225140 (37:735)
  • 11. A. Spalsbury. Perturbations in Müntz's theorem, J. Approx. Theory, 150(1) (2008), 48-68. MR 2381528 (2009e:41038)

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Additional Information

S. Waleed Noor
Affiliation: Abdus Salam School of Mathematical Sciences, New Muslim Town, Lahore, 54600, Pakistan
Email: waleed{\textunderscore}math@hotmail.com

Dan Timotin
Affiliation: Institute of Mathematics of the Romanian Academy, Calea Griviţei 21, Bucharest, Romania
Email: Dan.Timotin@imar.ro

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11681-8
PII: S 0002-9939(2012)11681-8
Keywords: Müntz space, embedding measure, lacunary sequence, Schatten–von Neumann classes
Received by editor(s): September 18, 2011
Published electronically: December 18, 2012
Communicated by: Richard Rochberg
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.