Spectral theory of ordinary differential equations

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Sparse spectral approximations for computing polynomial functionals

Fabio Nobile

We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral eigenfunctions th ...

EPFL-SB-MATHICSE2012

Finite Element Method on Riemann Surfaces and Applications to the Laplacian Spectrum

Marc Maintrot

The objective of this PhD thesis is the approximate computation of the solutions of the Spectral Problem associated with the Laplace operator on a compact Riemann surface without boundaries. A Riemann surface can be seen as a gluing of portions of the Hype ...

EPFL2012

On Sampling and Coding for Distributed Acoustic Sensing

Martin Vetterli, Emre Telatar, Robert Konsbruck

The issue of how to efficiently represent the data collected by a network of microphones recording spatio-temporal acoustic wave fields is addressed. Each sensor node in the network samples the sound field, quantizes the samples and transmits the encoded s ...

2012

Sup-norms of Eigenfunctions on Arithmetic Ellipsoids

Philippe Michel

Let B be a positive quaternion algebra, and let O subset of B be an Eichler order. There is associated, in a natural way, a variety X = X(O) the connected components of which are indexed by the ideal classes of O and are isomorphic to spheres. This variety ...

Oxford University Press2011

Frame Domain Signal Processing: Framework and Applications

Martin Vetterli, Amina Chebira

Besides basis expansions, frames representations play a key role in signal processing. We thus consider the problem of frame domain signal processing, which is more complex and challenging than transform domain processing. Examples of such processing aboun ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Spin-orbit coupling effects in the band structure of surface alloys

Luca Moreschini

At the surface of a solid, quantum mechanics allows the existence of two-dimensional Bloch waves as solutions of the Schrödinger equation. These "surface" states are interesting both for fundamental and practical reasons, and have been extensively explored ...

EPFL2009

Regularity in metric spaces

Serguei Timochine

Using arguments developed by De Giorgi in the 1950's, it is possible to prove the regularity of the solutions to a vast class of variational problems in the Euclidean space. The main goal of the present thesis is to extend these results to the more abstrac ...

EPFL2006

Variational reconstruction of scalar and vector images from non-uniform samples

Muthuvel Arigovindan

We address the problem of reconstructing scalar and vector functions from non-uniform data. The reconstruction problem is formulated as a minimization problem where the cost is a weighted sum of two terms. The first data term is the quadratic measure of go ...

EPFL2005

Power Spectra of Multipath Faded Pulse Trains

Andrea Ridolfi

We address the problem of modeling received pulse trains in a multipath fading channel and of computing their exact spectrum. We propose a model based on point processes. Such model is very general, simple and tractable and it allows to account for various ...

2005

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