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   -> Volume 7, Issue 1


Question: Wavelets and functional analysis
 
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Dave Dixon (dixon@agouti.ucr.edu)
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PostPosted: Thu Jan 08, 1998 3:46 am    
Subject: Question: Wavelets and functional analysis
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#23 Question: Wavelets and functional analysis

Hello. I am trying to understand some of the deeper mathematical
aspects of wavelets, particular how they relate to function classes,
etc. However, as a physicist I'm having a hard time getting my head
around the literature, such as Meyer's book. Are there any references
addressing this topic on a conceptual level, maybe assuming no more
than a knowledge of calculus, basic group theory, Fourier analysis,
etc? Something with some basic examples and pictures?

Some specific topics I'd like to get a better handle on:

- What are the various function classes, and where might specific ones prove
interesting (even approximately) in the real world?
- How/why do wavelets form "nice" bases for these function classes?
- How are wavelets related to measures of "smoothness"? How might
these measures be useful in quantifying aspects of a real signal or
image?
- What are the properties of an "unconditional basis"? Why does
unconditionality make us happy?
- What are things like the Wiener algebra, bump algebra, etc., and how
are they related to the above issues?

I realize that's a lot of ground to cover, and much of it may just be
a matter of looking at some understandable references on background
material before tackling Meyer and similar works. Or, if the experts
want to take a crack at answering some of these things in a basic
manner, I'd be willing to collate whatever info I get and put together
a WWW document for the non-experts. It seems to me that the work of
Donoho and others indicates that knowledge of these aspects is
important.

Thanks!

Dave
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