A family of singular semi-classical functionals
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.
scientific article; zbMATH DE number 1893650