GIAMBELLI’S FORMULA AND THE BEST CONSTANT OF SOBOLEV INEQUALITY IN ONE DIMENSIONAL EUCLIDEAN SPACE

Yoshinori Kametaka; Atsushi Nagai; Kohtaro Watanabe; Kazuo Takemura; Hiroyuki Yamagishi

doi:10.32219/isms.71.1_27

Yoshinori Kametaka, Atsushi Nagai, Kohtaro Watanabe, Kazuo Takemura, Hiroyuki Yamagishi

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Keywords: Green function, Sobolev inequality, Giambelli’s formula, Hurwitz polynomial, Schur polynomial

JOURNAL FREE ACCESS

2010 Volume 71 Issue 1 Pages 27-41

DOI https://doi.org/10.32219/isms.71.1_27

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Abstract

The best constant of Sobolev inequality associated with 2N-th order Hurwitz-type differential operator is computed. Giambelli’s formula which appears in representation theory of finite groups plays an important role.

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