Critical length for a Beurling type theorem

Michel Mehrenberger

Bollettino dell'Unione Matematica Italiana (2005)

  • Volume: 8-B, Issue: 1, page 251-258
  • ISSN: 0392-4041

Abstract

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In a recent paper [3] C. Baiocchi, V. Komornik and P. Loreti obtained a generalisation of Parseval's identity by means of divided differences. We give here a proof of the optimality of that theorem.

How to cite

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Mehrenberger, Michel. "Critical length for a Beurling type theorem." Bollettino dell'Unione Matematica Italiana 8-B.1 (2005): 251-258. <http://eudml.org/doc/195190>.

@article{Mehrenberger2005,
abstract = {In a recent paper [3] C. Baiocchi, V. Komornik and P. Loreti obtained a generalisation of Parseval's identity by means of divided differences. We give here a proof of the optimality of that theorem.},
author = {Mehrenberger, Michel},
journal = {Bollettino dell'Unione Matematica Italiana},
language = {eng},
month = {2},
number = {1},
pages = {251-258},
publisher = {Unione Matematica Italiana},
title = {Critical length for a Beurling type theorem},
url = {http://eudml.org/doc/195190},
volume = {8-B},
year = {2005},
}

TY - JOUR
AU - Mehrenberger, Michel
TI - Critical length for a Beurling type theorem
JO - Bollettino dell'Unione Matematica Italiana
DA - 2005/2//
PB - Unione Matematica Italiana
VL - 8-B
IS - 1
SP - 251
EP - 258
AB - In a recent paper [3] C. Baiocchi, V. Komornik and P. Loreti obtained a generalisation of Parseval's identity by means of divided differences. We give here a proof of the optimality of that theorem.
LA - eng
UR - http://eudml.org/doc/195190
ER -

References

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  1. AVDONIN, S. A. - IVANOV, S. A., Exponential Riesz bases of subspaces and divided differences, St. Petersburg Math. J., 13 (3) (2002), 339-351. Zbl0999.42018MR1850184
  2. BAIOCCHI, C. - KOMORNIK, V. - LORETI, P., Ingham type theorems and applications to control theory, Bol. Un. Mat. Ital. B (8), 2, no. 1 (1999), 33-63. Zbl0924.42022MR1794544
  3. BAIOCCHI, C. - KOMORNIK, V. - LORETI, P., Ingham-Beurling type theorems with weakened gap conditions, Acta Math. Hungar., 97 (1-2) (2000), 55-95. Zbl1012.42022MR1932795
  4. GRÖCHENIG, K. - RAZAFINJATOVO, H., On Landau’s necessary density conditions for sampling and interpolation of band-limited functions, J. London Math. Soc. (2), 54 (1996), 557-565. Zbl0893.42017MR1413898
  5. LANDAU, H. J., Necessary density conditions for sampling and interpolation of certain entire functions, Acta Math., 117 (1967), 37-52. Zbl0154.15301MR222554
  6. SEIP, K., On the Connection between Exponential Bases and Certains Related Sequences in L 2 ⁢ 2 ⁢ π , π , Journal of Functional Analysis, 130 (1995), 131-160. Zbl0872.46006MR1331980
  7. ULLRICH, D., Divided differences and system of nonharmonic Fourier series, Proc. Amer. Math. Soc., 80 (1980), 47-57. Zbl0448.42009MR574507
  8. YOUNG, R. M., An Introduction to Nonharmonic Fourier Series, Academic Press, New York, 1980. Zbl0981.42001MR591684

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