Borel matrix

Michel Weber

Commentationes Mathematicae Universitatis Carolinae (1995)

  • Volume: 36, Issue: 2, page 401-415
  • ISSN: 0010-2628

Abstract

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We study the Borel summation method. We obtain a general sufficient condition for a given matrix A to have the Borel property. We deduce as corollaries, earlier results obtained by G. M“uller and J.D. Hill. Our result is expressed in terms belonging to the theory of Gaussian processes. We show that this result cannot be extended to the study of the Borel summation method on arbitrary dynamical systems. However, in the L p -setting, we establish necessary conditions of the same kind by using Bourgain’s entropy criterion.

How to cite

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Weber, Michel. "Borel matrix." Commentationes Mathematicae Universitatis Carolinae 36.2 (1995): 401-415. <http://eudml.org/doc/247725>.

@article{Weber1995,
abstract = {We study the Borel summation method. We obtain a general sufficient condition for a given matrix $A$ to have the Borel property. We deduce as corollaries, earlier results obtained by G. M“uller and J.D. Hill. Our result is expressed in terms belonging to the theory of Gaussian processes. We show that this result cannot be extended to the study of the Borel summation method on arbitrary dynamical systems. However, in the $L^p$-setting, we establish necessary conditions of the same kind by using Bourgain’s entropy criterion.},
author = {Weber, Michel},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {Borel matrix; almost sure convergence; GB and GC sets; Gaussian processes; ergodic theorem; Borel matrix; Borel summation; Bourgain's entropy criterion},
language = {eng},
number = {2},
pages = {401-415},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Borel matrix},
url = {http://eudml.org/doc/247725},
volume = {36},
year = {1995},
}

TY - JOUR
AU - Weber, Michel
TI - Borel matrix
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1995
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 36
IS - 2
SP - 401
EP - 415
AB - We study the Borel summation method. We obtain a general sufficient condition for a given matrix $A$ to have the Borel property. We deduce as corollaries, earlier results obtained by G. M“uller and J.D. Hill. Our result is expressed in terms belonging to the theory of Gaussian processes. We show that this result cannot be extended to the study of the Borel summation method on arbitrary dynamical systems. However, in the $L^p$-setting, we establish necessary conditions of the same kind by using Bourgain’s entropy criterion.
LA - eng
KW - Borel matrix; almost sure convergence; GB and GC sets; Gaussian processes; ergodic theorem; Borel matrix; Borel summation; Bourgain's entropy criterion
UR - http://eudml.org/doc/247725
ER -

References

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