IJPAM: Volume 36, No. 4 (2007)

ON THE PARTIAL SUMS OF WAVELET PACKET SERIES

Firdous Ahmad Shah$^1$, Khalil Ahmad$^2$
$^{1,2}$Department of Mathematics
Jamia Millia Islamia (Central University)
New Delhi, 110025, INDIA
$^1$e-mail: fashah_jmi@yahoo.co.in
$^2$e-mail: khalil_ahmad49@yahoo.com


Abstract.It is shown that for a given distribution $f$ belonging to the Sobolev space ${\cal H}^{1/2}$, its partial sums of wavelet packet expansions behave like truncated versions of inverse Fourier transform of $\hat f$. Our result is sharp in the sense that such behavior no longer happens in general for ${\cal H}^{s}$ if $s<1/2.$

Received: March 5, 2007

AMS Subject Classification: 42C15, 40A30

Key Words and Phrases: multiresolution, wavelet packets, partial sums, Sobolev space

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 36
Issue: 4