On some classical type Sobolev orthogonal polynomials

Pencils of Semi-Infinite Matrices and Orthogonal Polynomials

“…In ref. [37] there was proposed a way to construct such systems of polynomials. Let p n x ðÞ ÈÉ ∞ n¼0 (p n has degree n and real coefficients) be orthogonal polynomials on a, b ½ ⊆  with respect to a weight function wx ðÞ :…”

“…In ref. [37] there were constructed families of Sobolev orthogonal polynomials on the real line, depending on an arbitrary finite number of complex parameters. Namely, we considered the following hypergeometric polynomials:…”

On a Family of Hypergeometric Sobolev Orthogonal Polynomials on the Unit Circle

“…Examples of such ideas are adding of Dirac deltas to the classical inner products and considering of coherent pairs of measures (see, e.g., [3,4] and references therein). In the present paper, we shall follow the same line: we shall develop the ideas from [20] to get some new hypergeometric polynomials and study their properties.…”

On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials

“…It is still under development and many aspects (such as the existence of recurrence relations) are hidden ( [5], [2]). It turned out that it is convenient to construct new families of Sobolev orthogonal polynomials by using known orthogonal polynomials on the real line (OPRL) or orthogonal polynomials on the unit circle (OPUC), see [16], [17]. Moreover, if a system of OPRL or OPUC is an eigenvector of a pencil of differential equations, then the associated Sobolev orthogonal polynomials have a similar property as well.…”