A family of singular semi-classical functionals (Q1866478)
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scientific article; zbMATH DE number 1893650
| Language | Label | Description | Also known as |
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| English | A family of singular semi-classical functionals |
scientific article; zbMATH DE number 1893650 |
Statements
A family of singular semi-classical functionals (English)
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15 July 2003
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The distributional equation of a semi-classical functional provides an efficient way to study the properties of the semi-classical OPS/functionals. A particular case of semi-classical OPS/functionals are the classical ones. For the distributional equation of classical functionals a regularity condition holds. The main result of the present paper is to show that in general such condition does not hold. The examples of semi-classical functionals that satisfy certains singular equation are built and an explicit representation of the corresponding monic orthogonal polynomials as well as the recurrence relations are found.
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semi-classical functionals
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distributional equation
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quasi-orthogonality
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regularity condition
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admissibility condition
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orthogonal polynomials
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