On completeness of orthogonal systems and Dirac deltas
type: Item
instance of: scholarly article
title: On completeness of orthogonal systems and Dirac deltas
zbMATH Open document ID: 0832.44007
DOI: 10.1016/0377-0427(93)E0272-N
author: Mario Pérez
author: Juan Luis Varona
published in: Journal of Computational and Applied Mathematics
publication date: 1996-03-05T00:00:00Z
review text: Given a positive measure \(\mu\) supported on a set \(\Omega \subseteq \mathbb{C}\), an orthonormal system \(\{ \varphi_n \}_{n\geq 0}\) and a point \(a\in \Omega\), the authors study the relationship among \(\mu( \{a \})\), the kernels \(K_n (a,a)= \sum_{k=1}^n \varphi_k (a) \overline {\varphi_k (a)}\) and the denseness of \(\text{span} \{\varphi_n \}_{n\geq 0}\) in \(L^2 (\mu)\) and in \(L^2 (\nu)\) where \(\nu= \mu+ M\delta_a\). An illustrative example is also considered.
reviewed by: Rekha Srivastava
Mathematics Subject Classification ID: 44A60
zbMATH DE Number: 804738
zbMATH Keywords: completeness
zbMATH Keywords: moment problem
zbMATH Keywords: orthonormal system
MaRDI profile type: Publication
cites work: Q5508534
cites work: Density questions in the classical theory of moments
cites work: Q4170993
cites work: Orthogonal polynomials
cites work: Q3849152
description: scientific article; zbMATH DE number 804738