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On the modification of non-regular linear functionals via addition of the Dirac delta function
-
Mabrouk Sghaier
and
Lamaa Khaled
Published/Copyright:
February 27, 2015
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.
Keywords: Orthogonal polynomials; Jacobi matrices; semiclassical
linear functionals; integral representations
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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- Frontmatter
- Existence of nontrivial solutions to quasilinear polyharmonic equations with critical exponential growth
- The one-dimensional heat equation in the Alexiewicz norm
- Qualitative analysis of a mathematical model for tumor growth under the effect of periodic therapy
- On the modification of non-regular linear functionals via addition of the Dirac delta function
Keywords for this article
Orthogonal polynomials;
Jacobi matrices;
semiclassical
linear functionals;
integral representations
Articles in the same Issue
- Frontmatter
- Existence of nontrivial solutions to quasilinear polyharmonic equations with critical exponential growth
- The one-dimensional heat equation in the Alexiewicz norm
- Qualitative analysis of a mathematical model for tumor growth under the effect of periodic therapy
- On the modification of non-regular linear functionals via addition of the Dirac delta function
