Concept

Locally integrable function

Related publications (29)

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Topological Structures on DMC spaces

Rajai Nasser

Two channels are said to be equivalent if they are degraded from each other. The space of equivalent channels with input alphabet X and output alphabet Y can be naturally endowed with the quotient of the Euclidean topology by the equivalence relation. We s ...

2017

Calderón–Zygmund estimates and non-uniformly elliptic operators

Maria Colombo

We consider a class of non-uniformly nonlinear elliptic equations whose model is given by -div(vertical bar Du vertical bar(p-2)Du a(x) vertical bar Du vertical bar(q-2)Du) = -div(vertical bar F vertical bar Fp-2 a(x)vertical bar F vertical bar Fq-2) where ...

2016

A reduced basis localized orthogonal decomposition

Assyr Abdulle, Patrick Henning

In this work we combine the framework of the Reduced Basis method (RB) with the framework of the Localized Orthogonal Decomposition (LOD) in order to solve parametrized elliptic multiscale problems. The idea of the LOD is to split a high dimensional Finite ...

2015

Lyapunov exponents of random walks in small random potential: the upper bound

Thomas Mountford, Jean-Christophe Mourrat

We consider the simple random walk on Z(d) evolving in a random i.i.d. potential taking values in [0, +infinity). The potential is not assumed integrable, and can be rescaled by a multiplicative factor lambda > 0. Completing the work started in a companion ...

Univ Washington, Dept Mathematics2015

Numerical approximation of the fractional Laplacian via hp-finite elements, with an application to image denoising

Jan Sickmann Hesthaven, Paolo Gatto

The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neumann map for a degenerate elliptic equation posed in the semi-infinite cylinder Ω × (0,∞). In fact, the Neumann trace on Ω involves a Muckenhoupt weight that ...

Springer Verlag2015

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

Exponential splines and minimal-support bases for curve representation

Michaël Unser, Philippe Thévenaz, Ricard Delgado Gonzalo

Our interest is to characterize the spline-like integer-shift-invariant bases capable of reproducing exponential polynomial curves. We prove that any compact-support function that reproduces a subspace of the exponential polynomials can be expressed as the ...

Elsevier2012

Reliable Circuit Design with Nanowire Arrays

Giovanni De Micheli, Mohamed Haykel Ben Jamaa

The emergence of different fabrication techniques of silicon nanowires (SiNWs) raises the question of finding a suitable architectural organization of circuits based on them. Despite the possibility of building conventional CMOS circuits with SiNWs, the ab ...

Springer2011

Moyennabilité et courbure

Martin Anderegg

As Avez showed (in 1970), the fundamental group of a compact Riemannian manifold of nonpositive sectional curvature has exponential growth if and only if it is not flat. After several generalizations from Gromov, Zimmer, Anderson, Burger and Shroeder, the ...

EPFL2010

Integrable Evolution Equations on Spaces of Tensor Densities and Their Peakon Solutions

Feride Tiglay

We study a family of equations defined on the space of tensor densities of weight lambda on the circle and introduce two integrable PDE. One of the equations turns out to be closely related to the inviscid Burgers equation while the other has not been iden ...

Springer Verlag2010