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Concept

Reflexive space

Related publications (27)

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

Optimization Over Banach Spaces: A Unified View on Supervised Learning and Inverse Problems

Shayan Aziznejad

In this thesis, we reveal that supervised learning and inverse problems share similar mathematical foundations. Consequently, we are able to present a unified variational view of these tasks that we formulate as optimization problems posed over infinite-di ...

EPFL2022

Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

EPFL2022

Linear Lipschitz and C-1 extension operators through random projection

Federico Stra

We construct a regular random projection of a metric space onto a closed doubling subset and use it to linearly extend Lipschitz and C-1 functions. This way we prove more directly a result by Lee and Naor [5] and we generalize the C-l extension theorem by ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2021

Convex optimization in sums of Banach spaces

Michaël Unser, Shayan Aziznejad

We characterize the solution of a broad class of convex optimization problems that address the reconstruction of a function from a finite number of linear measurements. The underlying hypothesis is that the solution is decomposable as a finite sum of compo ...

2021

Discretisation and continuity: The emergence of symbols in communication

Martin Alois Rohrmeier, Robert Lieck

Vocal signalling systems, as used by humans and various non-human animals, exhibit discrete and continuous properties that can naturally be used to express discrete and continuous information, such as distinct words to denote objects in the world and proso ...

2021

Global bifurcation at isolated singular points of the Hadamard derivative

Charles Stuart

Consider F is an element of C(RxX,Y) such that F(lambda, 0) = 0 for all lambda is an element of R, where X and Y are Banach spaces. Bifurcation from the line Rx{0} of trivial solutions is investigated in cases where F(lambda, center dot ) need not be Frech ...

2021

A Unifying Representer Theorem for Inverse Problems and Machine Learning

Michaël Unser

Regularization addresses the ill-posedness of the training problem in machine learning or the reconstruction of a signal from a limited number of measurements. The method is applicable whenever the problem is formulated as an optimization task. The standar ...

2021

Quenched convergence and strong local equilibrium for asymmetric zero-range process with site disorder

Thomas Mountford

We study asymmetric zero-range processes on Z with nearest-neighbour jumps and site disorder. The jump rate of particles is an arbitrary but bounded nondecreasing function of the number of particles. We prove quenched strong local equilibrium at subcritica ...

SPRINGER HEIDELBERG2020

The Error-Feedback Framework: Better Rates for SGD with Delayed Gradients and Compressed Updates

Sebastian Urban Stich, Sai Praneeth Reddy Karimireddy

We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two terms: (i) a stocha ...

Microtome Publishing2020

Group Approximation in Cayley Topology and Coarse Geometry, Part II: Fibred Coarse Embeddings

Georges Samarine

The objective of this series is to study metric geometric properties of disjoint unions of Cayley graphs of amenable groups by group properties of the Cayley accumulation points in the space of marked groups. In this Part II, we prove that a disjoint union ...

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

Hypomonotonicity of the Normal Cone and Proximal Smoothness

Grigory Ivanov

We study the properties of the normal cone to a proximally smooth set. We give a complete characterization of a proximally smooth set through the monotonicity properties of its normal cone in an arbitrary uniformly convex and uniformly smooth Banach space. ...

Heldermann Verlag2017

Representing groups against all odds

Maxime Gheysens

We investigate how probability tools can be useful to study representations of non-amenable groups. A suitable notion of "probabilistic subgroup" is proposed for locally compact groups, and is valuable to induction of representations. Nonamenable groups ad ...

EPFL2017

New Moduli For Banach Spaces

Grigory Ivanov

Modifying the moduli of supporting convexity and supporting smoothness, we introduce new moduli for Banach spaces which occur, for example, as lengths of catheti of right-angled triangles (defined via so-called quasiorthogonality). These triangles have two ...

Tusi Mathematical Research Group2017

Splines Are Universal Solutions of Linear Inverse Problems with Generalized TV Regularization

Michaël Unser, Julien René Fageot, John Paul Ward

Splines come in a variety of flavors that can be characterized in terms of some differential operator L. The simplest piecewise-constant model corresponds to the derivative operator. Likewise, one can extend the traditional notion of total variation by con ...

2017

Bifurcation at isolated singular points of the Hadamard derivative

Charles Stuart

For Banach spaces X and Y, we consider bifurcation from the line of trivial solutions for the equation F(lambda, u) = 0, where F : R x X -> Y with F(lambda, 0) = 0 for all lambda is an element of R. The focus is on the situation where F(lambda, center dot) ...

Royal Society of Edinburgh Scotland Foundation, Cambridge2014

Homogeneous Sobolev Metric of Order One on Diffeomorphism Groups on Real Line

Martins Bruveris

In this article we study Sobolev metrics of order one on diffeomorphism groups on the real line. We prove that the space equipped with the homogeneous Sobolev metric of order one is a flat space in the sense of Riemannian geometry, as it is isometric to an ...

Springer Verlag2014

A fixed point theorem for L1 spaces

Nicolas Monod

We prove a fixed point theorem for a family of Banach spaces, notably for L^1. Applications include the optimal answer to the "derivation problem" for group algebras which originated in the 1960s. ...

Springer-Verlag2012

Asymptotic linearity and Hadamard differentiability

Charles Stuart

For a mapping between Banach spaces, two weaker variants of the usual notion of asymptotic linearity are defined and explored. It is shown that, under inversion through the unit sphere, they correspond to Hadamard and weak Hadamard differentiability at the ...

2012

Related publications (27)