THE BEST CONSTANT OF SOBOLEV INEQUALITY WHICH CORRESPONDS TO SCHRÖDINGER OPERATOR WITH DIRAC DELTA POTENTIAL

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

doi:10.32219/isms.69.2_211

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

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Keywords: best constant, Sobolev inequality, Green function, reproducing kernel, Schrödinger operator, Dirac delta potential

JOURNAL FREE ACCESS

2009 Volume 69 Issue 2 Pages 211-225

DOI https://doi.org/10.32219/isms.69.2_211

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Abstract

We consider boundary value problems for the one-dimensional Schrödinger operator with Dirac delta potential. Green functions G(x, y) are constructed by using the symmetric orthogonalization method, and their aspects as reproducing kernel are also investigated. As an application, the best constants of the corresponding Sobolev inequalities is expressed as the maximum of the diagonal value G(y, y).

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