Titlebook: Algebraic Analysis of Differential Equations; from Microlocal Anal Takashi Aoki,Hideyuki Majima,Nobuyuki Tose Book 2008 Springer-Verlag Tok

Communal

Aesthete

顧客

https://doi.org/10.1007/978-3-319-06242-6In this paper we give examples of the resummation of transseries in partial differential equations using the language of the Z-transform. In so doing we illustrate the relationship between matched and exponential asymptotic approaches to the modelling of shock waves.

輕信

FOLLY

laxative

BLINK

Regular sequences associated with the Noumi-Yamada equations with a large parameterWe consider the system of algebraic equations that defines the leading terms of formal solutions to the Noumi-Yamada equations of even order and prove that the polynomial sequence associated with the system is a regular sequence.

acrimony

致命

enflame

The Borel transformWe formulate the Borel transform in terms of functional analysis, in particular in terms of Analytically Uniform (AU) spaces. This enables us to extend the ideas of Borel to functions of several complex variables. Combining these ideas with nonlinear Fourier analysis leads to a generalization of the convexity that appears in Borel’s work.