Open AccessRiesz systems and moment method in the study of viscoelasticity in one space dimension
Author(s) -
Luciano Pandolfi
Publication year - 2010
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2010.14.1487
Subject(s) - observability , controllability , dimension (graph theory) , interpolation (computer graphics) , moment (physics) , mathematics , riesz representation theorem , m. riesz extension theorem , viscoelasticity , moment problem , space (punctuation) , key (lock) , pure mathematics , riesz potential , mathematical analysis , computer science , physics , statistics , artificial intelligence , motion (physics) , computer security , classical mechanics , principle of maximum entropy , thermodynamics , operating system
In this paper we study the equation of linear viscoelasticity and we prove that two sequences of functions, naturally associated with this equation, are Riesz sequences in $L^2(0,T$ for a suitable time $T$. It is to be noted that these functions solve suitable Volterra integro-differential equation, are not sequence of exponentials and are not eigenfunctions of operators naturally associated to the system. In spite of this, these sequences of functions appear naturally when observability and controllability problems are reformulated in terms of suitable interpolation/moment problem