Related papers: On eigenmeasures under Fourier transform

We consider the Fourier restriction operators associated to certain degenerate curves in R^d for which the highest torsion vanishes. We prove estimates with respect to affine arclength and with respect to the Euclidean arclength measure on…

We study the multifractal analysis of self-similar measures arising from random homogeneous iterated function systems. Under the assumption of the uniform strong separation condition, we see that this analysis parallels that of the…

Let $E$ be a finite dimensional vector space over a local field, and $F$ be its dual. For a closed subset $X$ of $E$, and $Y$ of $F$, consider the space $D^{-\xi}(E;X,Y)$ of tempered distributions on $E$ whose support are contained in $X$…

Based on the recent developments in the irregular Riemann-Hilbert correspondence for holonomic D-modules and the Fourier-Sato transforms for enhanced ind-sheaves, we study the Fourier transforms of some irregular holonomic D-modules. For…

Shape-invariant signals under Fourier transform are investigated leading to a class of eigenfunctions for the Fourier operator. The classical uncertainty Gabor-Heisenberg principle is revisited and the concept of isoresolution in joint…

For an arbitrary Radon measure $\mu$ we estimate the integrated discrete curvature of $\mu$ in terms of its centred variant of Jones' beta numbers. We farther relate integrals of centred and non-centred beta numbers. As a corollary,…

The objective in this paper is to demonstrate that four of the most used techniques in applied mathematics, viz., Fourier series, Fourier transform, Laplace transform and the Fourier-Laplace transform can be introduced using eigenvalue…

This is an attempt of a comprehensive survey of the results in which estimates of the norms of linear means of multiple Fourier series, the Lebesgue constants, are obtained by means of estimating the Fourier transform of a function…

The Hilbert transform is a multiplier operator and is widely used in the theory of Fourier transforms. The Hilbert transform was the motivation for the development of modern harmonic analysis. Its discrete version is also widely used in…

Suppose $F$ is a self-affine set on $\mathbb{R}^d$, $d\geq 2$, which is not a singleton, associated to affine contractions $f_j = A_j + b_j$, $A_j \in \mathrm{GL}(d,\mathbb{R})$, $b_j \in \mathbb{R}^d$, $j \in \mathcal{A}$, for some finite…

We construct a version of Fourier transform for a class of non-commutative algebras over abelian varieties which include algebras of twisted differential operators generalizing the previous construction of Laumon (alg-geom/9603004) and of…

In this paper, we relate the framework of mod-$\phi$ convergence to the construction of approximation schemes for lattice-distributed random variables. The point of view taken here is that of Fourier analysis in the Wiener algebra, allowing…

This note gives a summary of ideas concerning Applied Fourier Analysis, mostly formulated for those who have to give such courses to engineers or mathematicians interested in real life applications. It tries to answer recurrent questions…

We consider measures supported on sets of irrational numbers possessing many consecutive partial quotients satisfying a condition based on the previous partial quotients. We show that under mild assumptions, such sets will always support…

We show that, for a natural class of rearrangement admissible spaces $X$ and $Y$, the Fourier operator is bounded between $X$ and $Y$ if and only if any operator of joint strong type $(1,\infty; 2,2)$ is also bounded between $X$ and $Y$. By…

We discuss some of the mathematical properties of the fractional derivative defined by means of Fourier transforms. We first consider its action on the set of test functions $\Sc(\mathbb R)$, and then we extend it to its dual set,…

We prove that supports of a wide class of temperate distributions with uniformly discrete support and spectrum on Euclidean spaces are finite unions of translations of full-rank lattices. This result is a generalization of the corresponding…

We study properties of temperate non-negative purely atomic measures in the Euclidean space such that the distributional Fourier transform of these measures are pure point ones. A connection between these measures and almost periodicity is…

We study Whittaker vectors (and Jacquet integrals) in the generalized principal series for a real reductive group. A functional equation for them is obtained. This allows to establish uniform estimates for their holomorphic extensions with…

Classical spectral analysis is based on the discrete Fourier transform of the auto-covariances. In this paper we investigate the asymptotic properties of new frequency domain methods where the auto-covariances in the spectral density are…