Geodesic
Borel matrix
Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 401-415 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 28D05, 40G10, 49A35, 60F15, 60G15
Keywords: Borel matrix; almost sure convergence; \text{\sl GB} and \text{\sl GC} sets; Gaussian processes 
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     author = {Weber, Michel},
     title = {Borel matrix},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     pages = {401--415},
     year = {1995},
     volume = {36},
     number = {2},
     mrnumber = {1357539},
     zbl = {0837.28014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMUC_1995_36_2_a17/}
}
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Weber, Michel. Borel matrix. Commentationes Mathematicae Universitatis Carolinae, Tome 36 (1995) no. 2, pp. 401-415. http://geodesic.mathdoc.fr/item/CMUC_1995_36_2_a17/