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Concept

Spaces of test functions and distributions

Related publications (14)

Positive Definite Completions and Continuous Graphical Models

Kartik Waghmare

This thesis concerns the theory of positive-definite completions and its mutually beneficial connections to the statistics of function-valued or continuously-indexed random processes, better known as functional data analysis. In particular, it dwells upon ...

EPFL2023

Explicit representations for Banach subspaces of Lizorkin distributions

Michaël Unser, Sebastian Jonas Neumayer

The Lizorkin space is well suited to the study of operators like fractional Laplacians and the Radon transform. In this paper, we show that the space is unfortunately not complemented in the Schwartz space. In return, we show that it is dense in C0(Double- ...

2023

Hyperbolic Fourier series

Maryna Viazovska

In this article we explain the essence of the interrelation described in [PNAS 118, 15 (2021)] on how to write explicit interpolation formula for solutions of the Klein-Gordon equation by using the recent Fourier pair interpolation formula of Viazovska and ...

arXiv2021

Topological Linear System Identification via Moderate Deviations Theory

Daniel Kuhn, Wouter Jongeneel, Tobias Sutter

Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such as stability or ...

2022

Non-smooth solutions in incompressible fluid dynamics

Luigi De Rosa

This work is devoted to the study of the main models which describe the motion of incompressible fluids, namely the Navier-Stokes, together with their hypodissipative version, and the Euler equations. We will mainly focus on the analysis of non-smooth weak ...

EPFL2021

Non-linear transfer function identification of pressure probes using Siren Disks

Jürg Alexander Schiffmann, Karim Magdi Zakaria Abdelrahman Shalash

This article presents a Siren Disk proof of concept for the dynamic excitation of pressure probes, and a method to reconstruct distorted signals due to pneumatic channels. Constraints in sensor installation require placing a pressure transducer distant fro ...

2018

Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth

Michaël Unser, John Paul Ward, Quy Ha Nguyen

The Poisson summation formula (PSF) describes the equivalence between the sampling of an analog signal and the periodization of its frequency spectrum. In engineering textbooks, the PSF is usually stated formally without explicit conditions on the signal f ...

2017

Stochastic partial differential equations driven by Lévy white noises : generalized random processes, random field solutions and regularity

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

Composite Self-Concordant Minimization

Volkan Cevher, Anastasios Kyrillidis, Quoc Tran Dinh

We propose a variable metric framework for minimizing the sum of a self-concordant function and a possibly non-smooth convex function endowed with a computable proximal operator. We theoretically establish the convergence of our framework without relying o ...

Massachusetts Institute of Technology Press2015

Generalized Poisson Summation Formula for Tempered Distributions

Michaël Unser, Quy Ha Nguyen

The Poisson summation formula (PSF), which relates the sampling of an analog signal with the periodization of its Fourier transform, plays a key role in the classical sampling theory. In its current forms, the formula is only applicable to a limited class ...

IEEE2015

The non-linear stochastic wave equation in high dimensions : existence, Hölder-continuity and Itô-Taylor expansion

Daniel Conus

The main topic of this thesis is the study of the non-linear stochastic wave equation in spatial dimension greater than 3 driven by spatially homogeneous Gaussian noise that is white in time. We are interested in questions of existence and uniqueness of so ...

EPFL2008

Analysis and numerical simulation of viscoelastic flows : deterministic and stochastic models

Andrea Bonito

Mathematical and numerical aspects of viscoelastic flows are investigated here. Two simplified mathematical models are considered. They are motivated by a splitting algorithm for solving viscoelastic flows with free surfaces. The first model is a simplifie ...

EPFL2006

Existence, uniqueness and regularity of solutions for a thermomechanical model of shape memory alloys

Aïda Timofte

This thesis is devoted to the study of a thermomechanical model describing the macroscopic behavior of shape memory alloys. The analyzed model takes into account the non-isothermal character of the phase transition, as well as the existence of the intrinsi ...

EPFL2004

Fast Eigenspace Approximation using Random Signals

Lionel Jérémie Martin, Johann Paratte

We focus in this work on the estimation of the first k eigenvectors of any graph Laplacian using filtering of Gaussian random signals. We prove that we only need k such signals to be able to exactly recover as many of the smallest eigenvectors, regardless ...

2016