SEMINARIO DE MATEMÁTICA APLICADA

Martes, 9 de febrero de 2016

12:00 h., Módulo 17 (antiguo C-XV) - Aula 520 (Depto. Matemáticas UAM)

Stefano Serra-Capizzano
Insubria University

The GLT class as a Generalized Fourier Analysis
and applications

Abstract:

Recently, the class of Generalized Locally Toeplitz (GLT) sequences has been introduced as a
generalization both of classical Toeplitz sequences and of variable coefficient differential operators
and, for every sequence of the class, it has been demonstrated that it is possible to give a
rigorous description of the asymptotic spectrum in terms of a function (the symbol) that can be
’easily’ identified.
This generalizes the notion of a symbol for differential operators (discrete and continuous) or for
Toeplitz sequences for which it is identified through the Fourier coefficients and is related to the
classical Fourier Analysis.
The GLT class has nice algebraic properties and indeed it has been proven that it is stable under
linear combinations, products, and inversion when the sequence which is inverted shows a
sparsely vanishing symbol. Furthermore, the GLT class virtually includes any approximation of partial
differential equations (PDEs) by local methods (Finite Difference, Finite Element, Isogeometric
Analysis and, based on this, we demonstrate that our results on GLT sequences can be used in a
PDE setting in various theoretical and applied directions
Departamento de Matem´ aticas. UAM
ICMAT. CSIC-UAM-UC3M-UCM