Concept

Open mapping theorem (functional analysis)

Related publications (11)

Positive Definite Completions and Continuous Graphical Models

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

Multikernel Regression with Sparsity Constraint

Michaël Unser, Shayan Aziznejad

In this paper, we provide a Banach-space formulation of supervised learning with generalized total-variation (gTV) regularization. We identify the class of kernel functions that are admissible in this framework. Then, we propose a variation of supervised l ...

2021

System for planning and/or providing neuromodulation, especially neurostimulation

Grégoire Courtine, Vincent Delattre, Miroslav Caban, Marco Capogrosso, Fabien Bertrand Paul Wagner, Karen Minassian

The present invention relates system for planning and/or providing neuromodulation (10), especially neurostimulation, comprising - a neurostimulator (24) comprising a least one electrode (22), - functional mapping module (38) configured and arranged such t ...

2019

On the convergence of stochastic primal-dual hybrid gradient

Volkan Cevher, Ahmet Alacaoglu

In this paper, we analyze the recently proposed stochastic primal-dual hybrid gradient (SPDHG) algorithm and provide new theoretical results. In particular, we prove almost sure convergence of the iterates to a solution and linear convergence with standard ...

2019

Non-convex, non-local functionals converging to the total variation

Hoài-Minh Nguyên

We present new results concerning the approximation of the total variation, integral(Omega)vertical bar del u vertical bar, of a function u by non-local, non-convex functionals of the form Lambda delta(u) = integral(Omega)integral(Omega)delta phi(vertical ...

Elsevier2017

Obstacles For Splitting Multidimensional Necklaces

Michal Lason

The well-known "necklace splitting theorem" of Alon (1987) asserts that every k-colored necklace can be fairly split into q parts using at most t cuts, provided k(q - 1)

Amer Mathematical Soc2015

Nondyadic and nonlinear multiresolution image approximations

Maria Arrate Munoz Barrutia

This thesis focuses on the development of novel multiresolution image approximations. Specifically, we present two kinds of generalization of multiresolution techniques: image reduction for arbitrary scales, and nonlinear approximations using other metrics ...

EPFL2002

Equations de type implicite avec contraintes

Chiara Tanteri

In this thesis we will treat the Dirichlet problem for systems of implicit equations, i.e. where Ω ⊂ Rn is an open set, u : Ω → Rm, Fi : Ω × Rm × Rm×n → R, m,n ≥ 1, are continuous functions and φ, the boundary datum, is given. At first we will be intereste ...

EPFL2000

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