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Ghost matrices and a characterization of symmetric Sobolev bilinear forms

Authors
Journal
Linear Algebra and its Applications
0024-3795
Publisher
Elsevier
Publication Date
Volume
431
Identifiers
DOI: 10.1016/j.laa.2009.02.014
Keywords
  • Orthogonal Polynomials
  • Moment Functional
  • Symmetric Bilinear Form
  • Ghost Function
  • Ghost Matrix

Abstract

Abstract In this paper, we characterize symmetric Sobolev bilinear forms defined on P × P , where P is the space of polynomials. More specifically we show that symmetric Sobolev bilinear forms, like symmetric matrices, can be re-written with a diagonal representation. As an application, we introduce the notion of a ghost matrix, extending some classic work of Stieltjes.

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