Biorthogonal exponential sequences with weight function $\exp (ax^2+ibx)$ on the real line and an orthogonal sequence of trigonometric functions
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- by Mohammad Masjed-Jamei PDF
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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 StieltjesβWigert 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 $(-\infty ,\infty )$.References
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Additional Information
- 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
- Received by editor(s): September 14, 2006
- Published electronically: November 1, 2007
- Communicated by: Carmen C. Chicone
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 136 (2008), 409-417
- MSC (2000): Primary 05E35, 42C05, 33C47
- DOI: https://doi.org/10.1090/S0002-9939-07-09139-3
- MathSciNet review: 2358478