Recovering the orthogonal polynomials from its specific spectral transformations

Abstract

In this work, the concept of quasi-type Kernel polynomials with respect to a moment functional is introduced. Difference equation satisfied by these polynomials along with the criterion for orthogonality conditions are discussed. Recovering the source orthogonal polynomial involving the linear spectral transformation is provided. This process involves an expression of ratio of kernel polynomials. Special cases of such ratios in terms of certain continued fractions are exhibited.Comment: 21 PAGE