Legendre Wavelet expansion of functions and their Approximations
DOI:
https://doi.org/10.23755/rm.v37i0.491Keywords:
Legendre Wavelet, Legendre Wavelet Expansion, Orthonormal basis, Legendre Wavelet Approximation .Abstract
In this paper , nine new Legendre wavelet estimators of functions
having bounded third and fourth derivatives have been obtained.These
estimators are new and best approximation in wavelet analysis. Legendre
wavelet estimator of a function f of bounded higher order derivatives is
better and sharper than the estimator of a function f of bounded less order
derivative.
References
A. Zygmund , Trigonometric Series Volume I, Cambridge University Press,1959.
H. N. Mhaskar, Polynomial operators and local smoothness classes on the unit interval, II," Jaen J. Approx., Vol. 1, No. 1(2009), pp. 1-25.
J. Morlet, G. Arens, E. Fourgeau and D. Giard, Wave propagation and sampling theory, part I; Complex signal and scattering in multilayer media,Geophysics 47(1982) No. 2, 203-221.
J. Morlet, G. Arens, E. Fourgeau and D. Giard, Wave propagation and sampling theory, part II; sampling theory complex waves, Geophysics 47(1982) no. 2, 222-236.
L. Debnath, Wavelet Transform and their applications, Birkhauser Bostoon,Massachusetts-2002.
P. Sablonniere, Rational Bernstein and spline approximation. A new approach, " Jaen J. Approx., Vol. 1, No. 1(2009), pp. 37-53.
R. A. Devore, Nonlinear Approximation, Acta Numerica, Vol. 7, Cambridge University Press,Cambridge(1998), pp. 51-150.
Shyam Lal and Susheel Kumar Best Wavelet Approximation of functionbelonging to Generalized Lipschitz Class using Haar Scaling function," ThaiJournal of Mathematics, Vol. 15(2017), No. 2, pp. 409-419.
Y. Meyer (1993)(Toulouse(1992))(Y. Meyer and S. Roques , eds) Frontieres,Gif-sur-Yvette, Wavelets their post and their future, Progress in Waveletanalysis and applications, pp. 9-18.
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