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Finiteness property for generalized abelian integrals
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We study the integrals of real functions which are finite compositions of globally
subanalytic maps and real power functions. These functions have finiteness properties
very similar to those of subanalytic functions. Our aim is to investigate how such
finiteness properties can remain when taking the integrals of such functions. The main
result is that for almost all power maps arising in a
x
λ
-function, its
integration leads to a non-oscillating function. This can be seen as a generalization of
Varchenko and Khovanskii’s finiteness theorems for abelian integrals.
Title: Finiteness property for generalized abelian integrals
Description:
We study the integrals of real functions which are finite compositions of globally
subanalytic maps and real power functions.
These functions have finiteness properties
very similar to those of subanalytic functions.
Our aim is to investigate how such
finiteness properties can remain when taking the integrals of such functions.
The main
result is that for almost all power maps arising in a
x
λ
-function, its
integration leads to a non-oscillating function.
This can be seen as a generalization of
Varchenko and Khovanskii’s finiteness theorems for abelian integrals.
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