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