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Regularity of fractal interpolation functions via wavelet transform
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Srijanani Anurag Prasad
Published/Copyright:
June 5, 2013
Abstract.
In the present paper, the regularity of a Fractal Interpolation Function (FIF) is studied using wavelet transform. The wavelet transform of FIF is obtained through two different methods. The first method uses the functional equation which FIF satisfies. By this method, it is shown that the FIF belongs to Lipschitz class of order 
, 
, under certain conditions on free parameters used in the construction of FIF. The second method is via Fourier transform of FIF. This approach gives the regularity of the FIF under certain conditions on free parameters. The Fourier transform of a FIF is also derived in this paper to facilitate the approach of wavelet transform of a FIF via Fourier transform.
Keywords: Fractal; interpolation function; wavelet transform; Fourier transform; functional equation
Received: 2013-02-07
Accepted: 2013-05-20
Published Online: 2013-06-05
Published in Print: 2013-06-01
© 2013 by Walter de Gruyter Berlin Boston
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Keywords for this article
Fractal;
interpolation function;
wavelet transform;
Fourier transform;
functional equation
Articles in the same Issue
- Masthead
- Erratum: Harmonic boundary value problems in a quarter ring domain [Adv. Pure Appl. Math. 3 (2012), 393–419]
- Dunkl kernel and Dunkl translation for a positive subsystem of orthogonal roots
- On orthogonal polynomials associated with rational perturbations of linear functional
- Multiple solutions for a class of p(x)-Kirchhoff type problems with Neumann boundary conditions
- A further application of power increasing sequences
- Regularity of fractal interpolation functions via wavelet transform
- Finite groups with some weakly s-semipermutable subgroups
- Stratification of the fourth secant variety of Veronese varieties via the symmetric rank
