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Concept

Pseudo-differential operator

Related publications (26)

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Victor Panaretos, Julien René Fageot, Matthieu Martin Jean-André Simeoni, Alessia Caponera

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

2022

Efficient Meso-Scale Modeling of Alkali-Silica-Reaction Damage in Concrete

Ali Falsafi

The alkali-silica reaction (ASR), also known as concrete cancer, is one of the most prevalent causes of concrete degradation. In this chemical reaction, amorphous silica in the aggregates reacts with alkalis in the pore solution. By absorbing water, hydrop ...

EPFL2022

Graph signal processing tailored for subgraph focus and community structure

Miljan Petrovic

Community structure in graph-modeled data appears in a range of disciplines that comprise network science. Its importance relies on the influence it bears on other properties of graphs such as resilience, or prediction of missing connections. Nevertheless, ...

EPFL2022

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

Characterization of image spaces of Riemann-Liouville fractional integral operators on Sobolev spaces W-m,W-p (omega)

Jan Sickmann Hesthaven

Fractional operators are widely used in mathematical models describing abnormal and nonlocal phenomena. Although there are extensive numerical methods for solving the corresponding model problems, theoretical analysis such as the regularity result, or the ...

SCIENCE PRESS2020

Spinning operators and defects in conformal field theory

Marco Meineri

We study the kinematics of correlation functions of local and extended operators in a conformal field theory. We present a new method for constructing the tensor structures associated to primary operators in an arbitrary bosonic representation of the Loren ...

Springer Nature2019

Generalized Norm-compatible Systems on Unitary Shimura Varieties

Mohamed Réda Boumasmoud

We define and study in terms of integral Iwahoriâ Hecke algebras a new class of geometric operators acting on the Bruhat-Tits building of connected reductive groups over p-adic fields. These operators, which we call U-operators, generalize the geometric n ...

EPFL2019

Atom-density representations for machine learning

Michele Ceriotti, Félix Benedito Clément Musil, Michael John Willatt

This has led to a proliferation of alternative ways to convert an atomic structure into an input for a machine-learning model. We introduce an abstract definition of chemical environments that is based on a smoothed atomic density, using a bra-ket notation ...

2019

Nonlinear Gyrokinetic Coulomb Collision Operator

Paolo Ricci, Rogério Manuel Cabete De Jesus Jorge, Baptiste Jimmy Frei

A gyrokinetic Coulomb collision operator is derived, which is particularly useful to describe the plasma dynamics at the periphery region of magnetic confinement fusion devices. The derived operator is able to describe collisions occurring in distribution ...

Cambridge University Press2019

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 ...

Springer Nature2019

Universality at large transverse spin in defect CFT

Marco Meineri

We study the spectrum of local operators living on a defect in a generic conformal field theory, and their coupling to the local bulk operators. We establish the existence of universal accumulation points in the spectrum at large s, s being the charge of t ...

Springer Nature2018

On sums of eigenvalues of elliptic operators on manifolds

Joachim Stubbe

We use the averaged variational principle introduced in a recent article on graph spectra [10] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of Kroger's bound ...

European Mathematical Soc2017

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

Gaussian versus Sparse Stochastic Processes : Construction, Regularity, Compressibility

Julien René Fageot

Although our work lies in the field of random processes, this thesis was originally motivated by signal processing applications, mainly the stochastic modeling of sparse signals. We develop a mathematical study of the innovation model, under which a signal ...

EPFL2017

Limiting absorption principle and well-posedness for the Helmholtz equation with sign changing coefficients

Hoài-Minh Nguyên

In this paper, we investigate the limiting absorption principle associated to and the well-posedness of the Helmholtz equations with sign changing coefficients which are used to model negative index materials. Using the reflecting technique introduced in [ ...

Elsevier2016

A generalized mountain-pass theorem: the existence of multiple critical points

Hans-Jörg Ruppen

We analyse the existence of multiple critical points for an even functional J : H -> R in the following context: the Hilbert space H can be split into an orthogonal sum H = Y circle plus Z in such a way that inf{J(u) : u is an element of Z and parallel to ...

Springer Heidelberg2016

Eigenfunction expansions of ultradifferentiable functions and ultradistributions

Aparajita Dasgupta

In this paper we give a global characterisation of classes of ultradi_erentiable functions and corresponding ultradistributions on a compact manifold X. The characterisation is given in terms of the eigenfunction expansion of an elliptic operator on X. Thi ...

2016

Left-inverses of fractional Laplacian and sparse stochastic processes

Michaël Unser

The fractional Laplacian (-Delta)(gamma/2) commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0 < gamma < d, its inver ...

Springer2012

Plenoptic based super-resolution for omnidirectional image sequences

Pascal Frossard, Pierre Vandergheynst, Luigi Bagnato

This paper addresses the reconstruction of high resolution omnidirectional images from a low resolution video acquired by an omnidirectional camera moving in a static scene. In order to exploit the additional information provided by the side images in the ...

2010

Exponential decay and Fredholm properties in second-order quasilinear elliptic systems

Charles Stuart, Hicham Georges Gebran

We consider second-order quasilinear elliptic systems on un-bounded domains in the setting of Sobolev spaces. We complete our earlier work on the Fredholm and properness properties of the associated differential operators by giving verifiable conditions fo ...

2010