Fourier Transforms of Measures and Algebraic Relations on Their Supports

Thomas W. Körner

Displaying similar documents to “Fourier Transforms of Measures and Algebraic Relations on Their Supports”

Invariant measures for the defocusing Nonlinear Schrödinger equation

Nikolay Tzvetkov (2008)

Annales de l’institut Fourier

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We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane $ℝ^{2}$ . We also prove an estimate giving some intuition to what may happen in $3$ dimensions.

The higher transvectants are redundant

Abdelmalek Abdesselam, Jaydeep Chipalkatti (2009)

Annales de l’institut Fourier

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Let $A, B$ denote generic binary forms, and let $𝔲_{r} = {(A, B)}_{r}$ denote their $r$ -th transvectant in the sense of classical invariant theory. In this paper we classify all the quadratic syzygies between the ${𝔲_{r}}$ . As a consequence, we show that each of the higher transvectants ${𝔲_{r} : r \geq 2}$ is redundant in the sense that it can be completely recovered from $𝔲_{0}$ and $𝔲_{1}$ . This result can be geometrically interpreted in terms of the incomplete Segre imbedding. The calculations rely upon the Cauchy exact sequence of $S L_{2}$ -representations,...

An explicit formula for the Hilbert symbol of a formal group

Floric Tavares Ribeiro (2011)

Annales de l’institut Fourier

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A Brückner-Vostokov formula for the Hilbert symbol of a formal group was established by Abrashkin under the assumption that roots of unity belong to the base field. The main motivation of this work is to remove this hypothesis. It is obtained by combining methods of ( $ϕ, Γ$ )-modules and a cohomological interpretation of Abrashkin’s technique. To do this, we build ( $ϕ, Γ$ )-modules adapted to the false Tate curve extension and generalize some related tools like the Herr complex with explicit formulas...

Fourier transform of the probability measures.

Vomişescu, Romeo (2002)

General Mathematics

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(Non-)weakly mixing operators and hypercyclicity sets

Frédéric Bayart, Étienne Matheron (2009)

Annales de l’institut Fourier

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We study the frequency of hypercyclicity of hypercyclic, non–weakly mixing linear operators. In particular, we show that on the space $ℓ^{1} (ℕ)$ , any sublinear frequency can be realized by a non–weakly mixing operator. A weaker but similar result is obtained for $c_{0} (ℕ)$ or $ℓ^{p} (ℕ)$ , $1 < p < \infty$ . Part of our results is related to some Sidon-type lacunarity properties for sequences of natural numbers.