Abstract and Applied Analysis
- Abstr. Appl. Anal.
- Volume 2014 (2014), Article ID 890456, 24 pages.
Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function
The family of nth order q-Legendre polynomials are introduced. They are shown to be obtainable from the Jacobi theta function and to satisfy recursion relations and multiplicatively advanced differential equations (MADEs) that are analogues of the recursion relations and ODEs satisfied by the nth degree Legendre polynomials. The nth order q-Legendre polynomials are shown to have vanishing kth moments for , as does the nth degree truncated Legendre polynomial. Convergence results are obtained, approximations are given, a reciprocal symmetry is shown, and nearly orthonormal frames are constructed. Conditions are given under which a MADE remains a MADE under inverse Fourier transform. This is used to construct new wavelets as solutions of MADEs.
Abstr. Appl. Anal., Volume 2014 (2014), Article ID 890456, 24 pages.
First available in Project Euclid: 27 February 2015
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Pravica, David W.; Randriampiry, Njinasoa; Spurr, Michael J. Smooth Wavelet Approximations of Truncated Legendre Polynomials via the Jacobi Theta Function. Abstr. Appl. Anal. 2014 (2014), Article ID 890456, 24 pages. doi:10.1155/2014/890456. https://projecteuclid.org/euclid.aaa/1425049836