Shoko Sasaki, Shun Takagi, Kouichi Takemura, “$q$-Middle Convolution and $q$-Painlevé Equation”, SIGMA, 2022, том 18,056, 21 стр.

Эта публикация цитируется в 2 статьях

$q$-Middle Convolution and $q$-Painlevé Equation

Shoko Sasaki^a, Shun Takagi^a, Kouichi Takemura^b

^a Department of Mathematics, Faculty of Science and Engineering, Chuo University, 1-13-27 Kasuga, Bunkyo-ku, Tokyo 112-8551, Japan
^b Department of Mathematics, Ochanomizu University, 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan

Аннотация: A $q$-deformation of the middle convolution was introduced by Sakai and Yamaguchi. We apply it to a linear $q$-difference equation associated with the $q$-Painlevé VI equation. Then we obtain integral transformations. We investigate the $q$-middle convolution in terms of the affine Weyl group symmetry of the $q$-Painlevé VI equation. We deduce an integral transformation on the $q$-Heun equation.

Ключевые слова: $q$-Painlevé equation, $q$-Heun equation, middle convolution, integral transformation.

MSC: 33E10, 34M55, 39A13

Поступила: 31 января 2022 г.; в окончательном варианте 8 июля 2022 г.; опубликована 20 июля 2022 г.

Язык публикации: английский

DOI: 10.3842/SIGMA.2022.056