arXiv subjects

Shingo Kamimoto

Publications and source records attributed to Shingo Kamimoto.

4 recordsLinked to original sources

arXiv2018

Multisummability in Carleman ultraholomorphic classes by means of nonzero proximate orders

We introduce a general multisummability theory of formal power series in Carleman ultraholomorphic classes. The finitely many levels of summation are determined by pairwise comparable, nonequivalent weight sequences admitting nonzero proximate orders and whose growth indices are distinct. Thus, we extend the powerful multisummability theory for finitely many Gevrey levels, developed by J.-P. Ramis, J. Écalle and W. Balser, among others. We provide both the analytical and cohomological approaches, and obtain a reconstruction formula for the multisum of a multisummable series by means of iterated generalized Laplace-like operators.

math.CV↗

arXiv2017

Iterated convolutions and endless Riemann surfaces

We discuss a version of Écalle's definition of resurgence, based on the notion of endless continuability in the Borel plane. We relate this with the notion of Ω-continuability, where Ω is a discrete filtered set, and show how to construct a universal Riemann surface X_Ω whose holomorphic functions are in one-to-one correspondence with Ω-continuable functions. We then discuss the Ω-continuability of convolution products and give estimates for iterated convolutions of the form \hatϕ_1*\cdots *\hatϕ_n. This allows us to handle nonlinear operations with resurgent series, e.g. substitution into a convergent power series.

math.DS↗

arXiv2016

Resurgent functions and nonlinear systems of differential and difference equations

The principal aim of this article is to establish an iteration method on the space of resurgent functions. We discuss endless continuability of iterated convolution products of resurgent functions and derive their estimates developing the method in arXiv:1610.05453. Using the estimates, we show the resurgence of formal series solutions of nonlinear differential and difference equations.

math.CA↗

arXiv2016

Nonlinear analysis with endlessly continuable functions

We give estimates for the convolution product of an arbitrary number of endlessly continuable functions. This allows us to deal with nonlinear operations for the corresponding resurgent series, e.g. substitution into a convergent power series.

math.DS↗