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0
votes
0answers
69 views

Fractional/complex powers of integrals

I'm wondering if there is a way to represent a fractional power of an integral as a function of the integrand in the following sense: The binomial theorem for complex/fractional exponents represents a ...
2
votes
0answers
107 views

Chen's iterated integrals and free loop space

I recently found out about Chen's iterated integrals for paths in a differentiable manifold, and I was wondering if an analogous construction exists for free loops, i.e. a set of variables one ...
3
votes
0answers
195 views

Restriction of iterated integrals

For a smooth manifold $X$, let $B_s(X)$ denote the space of iterated integrals of length at most $s$. Here we consider iterated integrals as functions on the path space $PX$. Fix a base point $x_0$ ...
13
votes
3answers
2k views

Understanding iterated integrals

I have encountered iterated integrals on papers dealing with multizeta values, polylogarithms etc.. Since then I am trying to figure out the motivations and purpose of the theory. It seems the ...