Construction of Majorizing Measures, Bernoulli Processes and Cotype.
M. Talagrand (1994)
Geometric and functional analysis
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M. Talagrand (1994)
Geometric and functional analysis
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Maciej Lewandowski (1989)
Mathematische Zeitschrift
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Nikolay Tzvetkov, Nicola Visciglia (2013)
Annales scientifiques de l'École Normale Supérieure
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Inspired by the work of Zhidkov on the KdV equation, we perform a construction of weighted Gaussian measures associated to the higher order conservation laws of the Benjamin-Ono equation. The resulting measures are supported by Sobolev spaces of increasing regularity. We also prove a property on the support of these measures leading to the conjecture that they are indeed invariant by the flow of the Benjamin-Ono equation.
Werner Linde (1988)
Mathematische Zeitschrift
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Tomasz Schreiber (2003)
Colloquium Mathematicae
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Lewis, Thomas M., Pritchard, Geoffrey (1999)
Electronic Communications in Probability [electronic only]
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Bogdan Mincer, Kazimierz Urbanik (1979)
Colloquium Mathematicum
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M. Talagrand (1996)
Geometric and functional analysis
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Waclaw Timoszyk (1974)
Colloquium Mathematicae
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T. Byczkowski (1981)
Studia Mathematica
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Artur Bartoszewicz (1978)
Colloquium Mathematicae
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Michel J. G. Weber (2012)
Colloquium Mathematicae
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We give two examples of periodic Gaussian processes, having entropy numbers of exactly the same order but radically different small deviations. Our construction is based on Knopp's classical result yielding existence of continuous nowhere differentiable functions, and more precisely on Loud's functions. We also obtain a general lower bound for small deviations using the majorizing measure method. We show by examples that our bound is sharp. We also apply it to Gaussian independent sequences...
Beloslav Riečan (1974)
Časopis pro pěstování matematiky
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