Dimension de Hausdorff du graphe d'une fonction continue: nouvelles majorations déterministes et minorations presque sûres

François Roueff

doi:10.1016/S0764-4442(01)01963-2

Dimension de Hausdorff du graphe d'une fonction continue: nouvelles majorations déterministes et minorations presque sûres

Translated title of the contribution: Hausdorff dimension of the graph of a continuous function: Deterministic upper bounds and almost sure lower bounds

François Roueff

Research output: Contribution to journal › Article › peer-review

Abstract

In this Note, we establish an upper bound of the Hausdorff dimension of the graph of a continuous function depending on its wavelet coefficients in a sufficiently regular wavelet basis. In particular, this bound is related to the Besov smoothness of the function. An almost sure lower bound of the same quantity is stated for some precise classes of random functions.

Translated title of the contribution	Hausdorff dimension of the graph of a continuous function: Deterministic upper bounds and almost sure lower bounds
Original language	French
Pages (from-to)	875-880
Number of pages	6
Journal	Comptes Rendus de l'Academie des Sciences - Series I: Mathematics
Volume	332
Issue number	10
DOIs	https://doi.org/10.1016/S0764-4442(01)01963-2
Publication status	Published - 1 Jun 2001

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title = "Dimension de Hausdorff du graphe d'une fonction continue: nouvelles majorations d{\'e}terministes et minorations presque s{\^u}res",

abstract = "In this Note, we establish an upper bound of the Hausdorff dimension of the graph of a continuous function depending on its wavelet coefficients in a sufficiently regular wavelet basis. In particular, this bound is related to the Besov smoothness of the function. An almost sure lower bound of the same quantity is stated for some precise classes of random functions.",

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AB - In this Note, we establish an upper bound of the Hausdorff dimension of the graph of a continuous function depending on its wavelet coefficients in a sufficiently regular wavelet basis. In particular, this bound is related to the Besov smoothness of the function. An almost sure lower bound of the same quantity is stated for some precise classes of random functions.

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DO - 10.1016/S0764-4442(01)01963-2

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JO - Comptes Rendus de l'Academie des Sciences - Series I: Mathematics

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IS - 10

ER -

Dimension de Hausdorff du graphe d'une fonction continue: nouvelles majorations déterministes et minorations presque sûres

Abstract

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