The Journal of the Indian Mathematical Society

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On the Rate of Convergence of Wavelet Expansions


Affiliations
1 Department of Mathematics, Govt. N.P.G. College of Science, Raipur (C.G.)-492010, India
     

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In this paper we estimate the rate of convergence of wavelet expansion of functions f ∈ Lp, 1 ≤ p ≤ ∞ at a point x. The pointwise and Lp results were obtained by Kelly, S. [4]. Our result generalizes her result.

Keywords

Wavelets, Convergence and Divergence of Series and Sequences, Rate of Convergence.
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  • G.H. Hardy, Divergent Series, Oxford, 1963.

  • Mallat, S., Multiresolution approximations and wavelet orthonormal bases of L2(R), Trans. of the Am.Math.Soc.,315(1989) no.1, 69-87.

  • Daubechies, I., Ten lectures on wavelets, CBMF-NSF series in applied Mathematics, SIAM,1992.

  • Kelly, S., Pointwise convergence for wavelet expansions, Ph.D. thesis, Washington University, St. Louis, 1992 .

  • Ruskai M.B., Beylkin G., Coifman R., Daubechies I., Mallat S., Meyer Y and Raphael L., eds., Wavelets and their applications, Jones and Bartlett, Boston, 1992.

  • E.C. Titchmarsh, The Theory of Functions, Oxford University Press, Second Edition, 1961.


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  • On the Rate of Convergence of Wavelet Expansions

Abstract Views: 341  |  PDF Views: 0

Authors

Varsha Karanjgaokar
Department of Mathematics, Govt. N.P.G. College of Science, Raipur (C.G.)-492010, India

Abstract


In this paper we estimate the rate of convergence of wavelet expansion of functions f ∈ Lp, 1 ≤ p ≤ ∞ at a point x. The pointwise and Lp results were obtained by Kelly, S. [4]. Our result generalizes her result.

Keywords


Wavelets, Convergence and Divergence of Series and Sequences, Rate of Convergence.

References