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A note on spectral properties of the $p$-adic tree

Authors
  • Klimek, Slawomir
  • Rathnayake, Sumedha
  • Sakai, Kaoru
Type
Preprint
Publication Date
Mar 10, 2015
Submission Date
Mar 10, 2015
Identifiers
DOI: 10.1063/1.4940339
Source
arXiv
License
Yellow
External links

Abstract

We study the spectrum of the operator $D^*D$, where the operator $D$, introduced in \cite{KMR}, is a forward derivative on the $p$-adic tree, a weighted rooted tree associated to $\mathbb Z_p$ via Michon's correspondence. We show that the spectrum is closely related to the roots of a certain $q-$hypergeometric function and discuss the analytic continuation of the zeta function associated with $D^*D$.

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