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Large Sieve Inequalities for Algebraic Trace Functions

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Modern image inpainting systems, despite the significant progress, often struggle with large missing areas, complex geometric structures, and high-resolution images. We find that one of the main reasons for that is the lack of an effective receptive field ...

IEEE COMPUTER SOC2022

Fourier non-uniqueness sets from totally real number fields

Martin Peter Stoller

Let K be a totally real number field of degree n >= 2. The inverse different of K gives rise to a lattice in Rn. We prove that the space of Schwartz Fourier eigenfunctions on R-n which vanish on the "component-wise square root" of this lattice, is infinite ...

EUROPEAN MATHEMATICAL SOC-EMS2022

Fourier uniqueness and interpolation in Euclidean space

Martin Peter Stoller

We prove that every Schwartz function in Euclidean space can be completely recovered given only its restrictions and the restrictions of its Fourier transform to all origin-centered spheres whose radii are square roots of integers. In particular, the only ...

EPFL2022

Finite free convolutions of polynomials

Adam Wade Marcus

We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric addi ...

SPRINGER HEIDELBERG2022

Fourier Tools

Paul Hurley, Sepand Kashani, Matthieu Martin Jean-André Simeoni

The FFT algorithm is a key pillar of modern numerical computing. This document is a collection of working notes on FFT-based algorithms. Efficient implementations of the former are made available through the pyFFS package. ...

2020

Correcting for non-periodic behaviour in perturbative experiments: application to heat pulse propagation and modulated gas-puff experiments

Federico Alberto Alfredo Felici, Cristian Galperti

This paper introduces a recent innovation in dealing with non-periodic behavior often referred to as transients in perturbative experiments. These transients can be the result from the unforced response due to the initial condition and other slow trends in ...

2020

Fourier movement primitives: an approach for learning rhythmic robot skills from demonstrations

Sylvain Calinon, Thibaut Antoine Kulak

Whether in factory or household scenarios, rhythmic movements play a crucial role in many daily-life tasks. In this paper we propose a Fourier movement primitive (FMP) representation to learn such type of skills from human demonstrations. Our approach take ...

2020

Fourier could be a data scientist: From graph Fourier transform to signal processing on graphs

Pierre Vandergheynst, Benjamin Ricaud, Nicolas Tremblay

The legacy of Joseph Fourier in science is vast, especially thanks to the essential tool that the Fourier transform is. The flexibility of this analysis, its computational efficiency and the physical interpretation it offers makes it a cornerstone in many ...

ELSEVIER FRANCE-EDITIONS SCIENTIFIQUES MEDICALES ELSEVIER2019

This chapter presents an overview of techniques used for the analysis, edition, and synthesis of time series, with a particular emphasis on motion data. The use of mixture models allows the decomposition of time signals as a superposition of basis function ...

Springer2019

Harmonic analysis and mean field theory

Denis Karateev

We review some aspects of harmonic analysis for the Euclidean conformal group, including conformally-invariant pairings, the Plancherel measure, and the shadow transform. We introduce two efficient methods for computing these quantities: one based on weigh ...

Springer2019