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Jacobi-type polynomials under an indefinite inner product

Published online by Cambridge University Press:  14 November 2011

Angelo B. Mingarelli  and
Allan M. Krall
Angelo B. Mingarelli
Affiliation:
Department of Mathematics, University of Ottawa, Ottawa, Ontario K1N9B4, Canada
Allan M. Krall
Affiliation:
McAllister Building, University Park, Pennsylvania 16802, U.S.A
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Synopsis

The polynomials which are orthogonal with respect to

when α> – 1, M>0 are considered when α<–1 and/or M<0. The Cauchy regularization of 〈·, ·〉 provides orthogonality and generates a Pontrjagin (Krein) space spanned by the polynomials. The polynomials are eigenfunctions associated with a self-adjoint, fourth order differential operator.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 90 , Issue 1-2 , 1981 , pp. 147 - 153
Copyright
Copyright © Royal Society of Edinburgh 1981

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