Generalized coherent pairs

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A pair of quasi-definite moment functionals {u(0),u(1)} is a generalized coherent pair if monic orthogonal polynomials {Pn(x)}(n=0)(proportional to), and {R-n(x)}(n=0)(infinity), relative to u(0) and u(1), respectively, satisfy a relation R-n(x) = 1/n+1 P'(n+1)(x)- sigma (n)/n P'(n)(x)-tau (n-1)/n-1 P'(n-1)(X), n greater than or equal to2 where sigma (n) and tau (n) are arbitrary constants, which may be zero. If {u(0),u(1)} is a generalized coherent pair, then u(0) and u(1) must be semiclassical. We find conditions under which either u(0) or u(1) is classical. In such a case, we also determine the types of the "companion" moment functionals. Also some illustrating examples and two ways of generating generalized coherent pairs are given. We also discuss the corresponding Sobolev orthogonal polynomials, (C) 2001 Academic Press.
Publisher
ACADEMIC PRESS INC
Issue Date
2001-01
Language
English
Article Type
Article
Keywords

ORTHOGONAL POLYNOMIALS

Citation

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, v.253, no.2, pp.482 - 514

ISSN
0022-247X
URI
http://hdl.handle.net/10203/83793
Appears in Collection
MA-Journal Papers(저널논문)
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