Memorias de investigación
Research Publications in journals:
A Characterization of Polynomial Density on Curves via Matrix Algebra
Year:2019

Research Areas
  • Mathematics

Information
Abstract
In this work, our aim is to obtain conditions to assure polynomial approximation in Hilbert spaces L2(m), with m a compactly supported measure in the complex plane, in terms of properties of the associated moment matrix with the measure m. To do it, in the more general context of Hermitian positive semidefinite matrices, we introduce two indexes, g(M) and l(M), associated with different optimization problems concerning theses matrices. Our main result is a characterization of density of polynomials in the case of measures supported on Jordan curves with non-empty interior using the index g and other specific index related to it. Moreover, we provide a new point of view of bounded point evaluations associated with a measure in terms of the index g that will allow us to give an alternative proof of Thomson?s theorem, by using these matrix indexes. We point out that our techniques are based in matrix algebra tools in the framework of Hermitian positive definite matrices and in the computation of certain indexes related to some optimization problems for infinite matrices.
International
Si
JCR
Si
Title
Mathematics
ISBN
22277390
Impact factor JCR
1,747
Impact info
Volume
10.3390/MATH7121231
Journal number
From page
1
To page
12
Month
SIN MES
Ranking
Participants

Research Group, Departaments and Institutes related
  • Creador: Centro o Instituto I+D+i: Centro de Investigación en Simulación Computacional