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Exponentials of de Branges–Rovnyak kernels

Part of: Special matrices

Published online by Cambridge University Press:  03 June 2021

Shuhei Kuwahara  and
Michio Seto
Shuhei Kuwahara
Affiliation:
Sapporo Seishu High School, Sapporo, Japan e-mail: s.kuwahara@sapporoseishu.ed.jp
Michio Seto*
Affiliation:
Department of Mathematics, National Defense Academy, Yokosuka, Japan
*
e-mail: mseto@nda.ac.jp
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Abstract

In this note, we give a new property of de Branges–Rovnyak kernels. As the main theorem, it is shown that the exponential of de Branges–Rovnyak kernel is strictly positive definite if the corresponding Schur class function is nontrivial.

Keywords

de Branges–Rovnyak kernelpositive definite kernelreproducing kernel Hilbert space

MSC classification

Secondary: 15B48: Positive matrices and their generalizations; cones of matrices
Type
Article
Information
Canadian Mathematical Bulletin , Volume 65 , Issue 2 , June 2022 , pp. 447 - 455
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Copyright
© Canadian Mathematical Society 2021

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