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The Wavelet Digest
   -> Volume 2, Issue 8

Question regarding a proof in Daubechies' book
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Samir Chettri, Faculty of Technology, Kanazawa University, Japan

PostPosted: Fri Nov 29, 2002 3:30 pm    
Subject: Question regarding a proof in Daubechies' book
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Question regarding a proof in Daubechies' book

Hello wavelet-folks:

Proposal: Why don't we change the wavelet digest name to WAVELETTERS.

Now that we have gotten the jokes out of the way, on to more serious
matters. I'm reading Daubechies book 10 LECTURES ON WAVELETS.
On page 153-154 is a proof of
int[ dx x^^l f(x) ] = 0 for l = 0,1, ...., m

(i.e., regularity of wavelets).
I've followed the proof except for one part of equation 5.5.4 (page 154)
The second term of 5.5.4 is written as

' | l ~ l
C | dy (1 + |y| ) | f (2 y) |

The first and second term of 5.5.4 (only the second term is written above)
is obtained from the second term of 5.5.2. I understand how the first
term of 5.5.4 was obtained. However it is not clear to me how the
second term (as written above) was obtained.

Could someone kindly help me.

Samir Chettri

Note from the editor:
Thank you very much for your suggestion. Actually, the name "Waveletter"
has been suggested to us by several people already and personally I feel
it is a much better name then "Wavelet Digest". We are currently considering
to restructure the setup of the digest and this will most likely be one of
the changes.
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