Proceedings of the American Mathematical Society

Biorthogonal exponential sequences with weight function $\exp(ax^2+ibx)$ on the real line and an orthogonal sequence of trigonometric functions

Author(s): Mohammad Masjed-Jamei
Journal: Proc. Amer. Math. Soc. 136 (2008), 409-417.
MSC (2000): Primary 05E35, 42C05, 33C47
Posted: November 1, 2007
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Abstract: Some orthogonal functions can be mapped onto other orthogonal functions by the Fourier transform. In this paper, by using the Fourier transform of Stieltjes-Wigert polynomials, we derive a sequence of exponential functions that are biorthogonal with respect to a complex weight function like $\exp(q_1(ix+p_1)^2+q_2(ix+p_2)^2)$ on $(-\infty,\infty)$ . Then we restrict these introduced biorthogonal functions to a special case to obtain a sequence of trigonometric functions orthogonal with respect to the real weight function $\exp(-qx^2)$ on $(-\infty,\infty)$ .

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 05E35, 42C05, 33C47

Mohammad Masjed-Jamei
Affiliation: Department of Applied Mathematics, K. N. Toosi University of Technology, P.O. Box 15875-4416, Tehran, Iran
Email: mmjamei@aut.ac.ir, mmjamei@yahoo.com

DOI: 10.1090/S0002-9939-07-09139-3
PII: S 0002-9939(07)09139-3
Keywords: Stieltjes--Wigert polynomials, Fourier transform, Parseval identity, normal and log-normal distributions.
Received by editor(s): September 14, 2006
Posted: November 1, 2007
Communicated by: Carmen C. Chicone
Copyright of article: Copyright 2007, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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