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Modifications of quasi-definite linear functionals via addition of delta and derivatives of delta Dirac functions |
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| Authors: | Álvarez-Nodarse J Arvesú F Marcellán |
| Institution: | a Departamento de Análisis Matemático, Universidad de Sevilla, Apdo. 1160, E-41080 Sevilla, Spain b Instituto Carlos I de Física Teórica y Computacional, Universidad de Granada, E-18071, Granada, Spain c Departamento de Matemáticas, E.P.S., Universidad Carlos III de Madrid, Ave. Universidad 30, E-28911, Leganés, Madrid, Spain d Ave. Universidad 30, E-28911, Leganés, Madrid, Spain |
| Abstract: | We consider the general theory of the modifications of quasi-definite linear functionals by adding discrete measures. We analyze the existence of the corresponding orthogonal polynomial sequences with respect to such linear functionals. The three-term recurrence relation, lowering and raising operators as well as the second order linear differential equation that the sequences of monic orthogonal polynomials satisfy when the linear functional is semiclassical are also established. A relevant example is considered in details. |
| Keywords: | Hypergeometric functions quasi-definite linear functional classical polynomials kernels orthogonal polynomials |
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