Geodesic
On Billard's Theorem for Random Fourier Series
Guy Cohen1 ; Christophe Cuny2
1 Department of Mathematics Ben Gurion University P.O.B. 653 841105 Beer Sheva, Israel and Erwin Schrödinger Institute Boltzmanngasse 9 A-1090 Wien, Austria
2 Department of Mathematics University of New Caledonia Equipe ERIM B.P. 4477 F-98847 Noumea Cedex, France
Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 1, pp. 39-53 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We show that Billard's theorem on a.s. uniform convergence of random Fourier series with independent symmetric coefficients is not true when the coefficients are only assumed to be centered independent. We give some necessary or sufficient conditions to ensure the validity of Billard's theorem in the centered case.
DOI : 10.4064/ba53-1-5
Keywords: billards theorem uniform convergence random fourier series independent symmetric coefficients coefficients only assumed centered independent necessary sufficient conditions ensure validity billards theorem centered

Guy Cohen 1 ; Christophe Cuny 2

1 Department of Mathematics Ben Gurion University P.O.B. 653 841105 Beer Sheva, Israel and Erwin Schrödinger Institute Boltzmanngasse 9 A-1090 Wien, Austria
2 Department of Mathematics University of New Caledonia Equipe ERIM B.P. 4477 F-98847 Noumea Cedex, France 
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Guy Cohen; Christophe Cuny. On Billard's Theorem for Random Fourier Series. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 53 (2005) no. 1, pp. 39-53. doi: 10.4064/ba53-1-5

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