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GómezUllate Otaiza, David and Kamran, Niky and Milson, Robert (2009) An extended class of orthogonal polynomials defined by a SturmLiouville problem. Journal of mathematical analysis and applications, 359 (1). pp. 352369. ISSN 0022247X

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Official URL: http://dx.doi.org/10.1016/j.jmaa.2009.05.052
URL  URL Type 

http://www.sciencedirect.com  Publisher 
http://arxiv.org/abs/0807.3939  Organisation 
Abstract
We present two infinite sequences of polynomial eigenfunctions of a SturmLiouville problem. As opposed to the classical orthogonal polynomial systems, these sequences start with a polynomial of degree one. We denote these polynomials as X(1)Jacobi and X(1)Laguerre and we prove that they are orthogonal with respect to a positive definite inner product defined over the compact interval [1, 1] or the halfline [0, infinity), respectively, and they are a basis of the corresponding L(2) Hilbert spaces. Moreover, we prove a converse statement similar to Bochner's theorem for the classical orthogonal polynomial systems: if a selfadjoint secondorder operator has a complete set of polynomial eigenfunctions {p(i)}(i=1)(infinity), then it must be either the X(1)Jacobi or the X(1)Laguerre SturmLiouville problem. A Rodriguestype formula can be derived for both of the X(1) polynomial sequences.
Item Type:  Article 

Additional Information:  © 2009 Elsevier Inc. All rights reserved. 
Uncontrolled Keywords:  Differentialequation; Bochner; Theorem 
Subjects:  Sciences > Physics > PhysicsMathematical models Sciences > Physics > Mathematical physics 
ID Code:  30809 
Deposited On:  15 Jun 2015 08:54 
Last Modified:  10 Dec 2018 15:09 
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