🚀 go-pugleaf

In article <BvoqI9.JFr@nic.umass.edu> S2822338@deimos.ucc.umass.edu (s2822338) writes:
>> I would appreciate it if someone could post or mail me the definition
>> of a "non-analytic distribution", apparently associated 
>> with a fractal support.  Let me state the context of my question:
>...
>> Does someone know of a book or article which deals with the 
>> calculus of such distributions?

If you have some mathematical background, Rudin's Real and Complex Analysis
will do. If you really know your math, then you will be able to go to 
Ma~ne's Ergodic Theory and Differentiable Dynamics. 

>wouldn't "non-analytic" imply that there would have to be some OTHER method of
>"figuring it all out" other than calculation... therefore no calculus per se
>would exist... or at least we'd have to look at something BESIDES the
>calculations, not necessarily to their exclusion...

"Calculus" is not equal to "calculations", and "Analysis" (as a branch of
mathematics) has nothing to do with "figuring it all out"... they were named
so centuries ago and the names remain.

A function is analytic in a domain iff you can expand it in Taylor series,
and the radius of convergence of this series is nonzero inside the domain.
That is, an analytic function has an infinite number of derivatives, and
you can locally know the function from the derivatives at one single 
point. 

Fractals are nonanalytic because they are non-differentiable everywhere. 
The converse is not entirely true. 

Best Regards,
Marcelo Magnasco
marcelo@mjf.rockefeller.edu	magnasco@research.nj.nec.com