The norm of the Fourier transform on finite abelian groups

John Gilbert; Ziemowit Rzeszotnik

Displaying similar documents to “The norm of the Fourier transform on finite abelian groups”

Uncertainty principles for the Schrödinger equation on Riemannian symmetric spaces of the noncompact type

Angela Pasquale, Maddala Sundari (2012)

Annales de l’institut Fourier

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Let $X$ be a Riemannian symmetric space of the noncompact type. We prove that the solution of the time-dependent Schrödinger equation on $X$ with square integrable initial condition $f$ is identically zero at all times $t$ whenever $f$ and the solution at a time $t_{0} > 0$ are simultaneously very rapidly decreasing. The stated condition of rapid decrease is of Beurling type. Conditions respectively of Gelfand-Shilov, Cowling-Price and Hardy type are deduced.

Fourier Transforms of Measures and Algebraic Relations on Their Supports

Thomas W. Körner (2009)

Annales de l’institut Fourier

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We investigate the relation between the rate of decrease of a Fourier transform and the possible algebraic relations on its support.

Remarks on the Fundamental Solution to Schrödinger Equation with Variable Coefficients

Kenichi Ito, Shu Nakamura (2012)

Annales de l’institut Fourier

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We consider Schrödinger operators $H$ on $ℝ^{n}$ with variable coefficients. Let $H_{0} = - \frac{1}{2} ▵$ be the free Schrödinger operator and we suppose $H$ is a “short-range” perturbation of $H_{0}$ . Then, under the nontrapping condition, we show that the time evolution operator: $e^{- i t H}$ can be written as a product of the free evolution operator $e^{- i t H_{0}}$ and a Fourier integral operator $W (t)$ which is associated to the canonical relation given by the classical mechanical scattering. We also prove a similar result for the wave operators....

Analysis of two step nilsequences

Bernard Host, Bryna Kra (2008)

Annales de l’institut Fourier

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Nilsequences arose in the study of the multiple ergodic averages associated to Furstenberg’s proof of Szemerédi’s Theorem and have since played a role in problems in additive combinatorics. Nilsequences are a generalization of almost periodic sequences and we study which portions of the classical theory for almost periodic sequences can be generalized for two step nilsequences. We state and prove basic properties for two step nilsequences and give a classification scheme for them. ...

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,...