Q-analogue of summability of formal solutions of some linear q-difference-differential equations

Hidetoshi Tahara, Hiroshi Yamazawa

研究成果: Article査読

9 被引用数 (Scopus)

抄録

Let q > 1. The paper considers a linear q-difference-differential equation: it is a q-difference equation in the time variable t, and a partial differential equation in the space variable z. Under suitable conditions and by using q-Borel and q-Laplace transforms (introduced by J.-P. Ramis and C. Zhang), the authors show that if it has a formal power series solution X(t; z ) one can construct an actual holomorphic solution which admits X(t; z ) as a q-Gevrey asymptotic expansion of order 1.

本文言語English
ページ(範囲)713-738
ページ数26
ジャーナルOpuscula Mathematica
35
5
DOI
出版ステータスPublished - 2015

ASJC Scopus subject areas

  • 数学 (全般)

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