Related papers: The restricted discrete Fourier transform
The search for a canonical set of eigenvectors of the discrete Fourier transform has been ongoing for more than three decades. The goal is to find an orthogonal basis of eigenvectors which would approximate Hermite functions -- the…
Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat harmonic manifolds of non-positive curvature and, in particular all known examples of harmonic manifolds except…
Using interpolation properties of non-commutative L^p-spaces associated with an arbitrary von Neumann algebra, we define a L^p-Fourier transform 1 <= p <= 2 on locally compact quantum groups. We show that the Fourier transform determines a…
We present the Fast Newton Transform (FNT), an algorithm for performing $m$-variate Newton interpolation in downward closed polynomial spaces with time complexity $\mathcal{O}(|A|m\overline{n})$. Here, $A$ is a downward closed set of…
In this paper we consider the problem of approximating function evaluations $f(\boldsymbol x_j)$ at given nonequispaced points $\boldsymbol x_j$, $j=1,\dots N$, of a bandlimited function from given values $\hat{f}(\boldsymbol k)$,…
Suppose that A is a subset of F_2^n of density as close to 1/3 as possible. We show that the A(F_2^n)-norm (that is the sum of the absolute values of the Fourier transform) of the characterstic function of A is bounded below by an absolute…
We present an algorithm for the forward propagation of intervals through the discrete Fourier transform. The algorithm yields best-possible bounds when computing the amplitude of the Fourier transform for real and complex valued sequences.…
We improve the exponent for the discrete Fourier restriction to the $n$ dimensional sphere, from $p=\frac{2(n+1)}{n-3}$ to $p=\frac{2n}{n-3}$, when $n\ge 4$.
Methods from soft-collinear effective theory are used to perform the threshold resummation of Sudakov logarithms for the deep-inelastic structure function F_2(x,Q^2) in the endpoint region x->1 directly in momentum space. An explicit…
For multi-variable finite measure spaces, we present in this paper a new framework for non-orthogonal $L^2$ Fourier expansions. Our results hold for probability measures $\mu$ with finite support in $\mathbb{R}^d$ that satisfy a certain…
The Fourier transform of a bounded measurable function, $f$, on the real line is shown to be the second distributional derivative of a H\"older continuous function. The Fourier transform is written as the difference of $\int_{-1}^1…
The complex exponentials with integer frequencies form a basis for the space of square integrable functions on the unit interval. We analyze whether the basis property is maintained if the support of the complex exponentials is restricted…
This paper presents a family of Fourier eigenfunctions indexed by the space dimension d. These eigenfunctions are radial and built upon some generalized exponential integral function. For d=1,2,3, they are integrable or square integrable…
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…
The paper is devoted to interrelation between the zeta distribution and the Radon transform on the space of $n \times m$ real matrices. We present a self-contained proof of the Fourier transform formula for this distribution. Our method…
We prove Fourier restriction estimates to arbitrary compact $C^{N}$ curves for any $N > d$ in the (sharp) Drury range, using a power of the affine arclength measure as a mitigating factor. In particular, we make no nondegeneracy assumption…
We introduce the concepts of the Fourier transform and convolution generated by an arbitrary restriction of the differentiation operator in the space $L_{2}(0,b).$ In contrast to the classical convolution, the introduced convolution…
We prove mapping properties of pseudodifferential operators with rough symbols on Hardy spaces for Fourier integral operators. The symbols $a(x,\eta)$ are elements of $C^{r}_{*}S^{m}_{1,\delta}$ classes that have limited regularity in the…
Inspired by work of Montgomery on Fourier series and Donoho-Strak in signal processing, we investigate two families of rearrangement inequalities for the Fourier transform. More precisely, we show that the $L^2$ behavior of a Fourier…
The strong dual space of linear continuous functionals on a weighted space G of infinitely differentiable functions defined on the real line is described in terms of their Fourier-Laplace transforms.