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Licensed Unlicensed Requires Authentication Published by De Gruyter February 27, 2015

On the modification of non-regular linear functionals via addition of the Dirac delta function

  • Mabrouk Sghaier EMAIL logo and Lamaa Khaled

Abstract

A linear functional (form) v is called regular if there exists a sequence of polynomials {Sn}n≥0 with deg Sn = n which is orthogonal with respect to v. The linear functional v˜ = S1v is not regular. We study properties of the linear functional u satisfying u = λv˜ + δa, where a ∈ ℂ and λ ∈ ℂ - {0}. Necessary and sufficient conditions are given for the regularity of the linear functional u. The corresponding tridiagonal matrices and associated polynomials are also studied. A study of the semiclassical character of the found families is done. We conclude by giving some examples.

MSC: 33C45; 42C05

Thanks are due to the referee for his helpful suggestions and comments that greatly contributed to improve the presentation of the manuscript.

Received: 2014-9-28
Revised: 2015-2-15
Accepted: 2015-2-16
Published Online: 2015-2-27
Published in Print: 2015-1-1

© 2015 by De Gruyter

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