Spectral dimension of spheres

Source
Communications in Algebra
ISSN
00927872
Date Issued
2020-06-02
Author(s)
DOI
Volume
48
Issue
6
Abstract
In this paper, we associate a growth graph to a homogeneous space of a compact group. Under certain assumptions, we show that the spectral dimension of a homogeneous space is greater than or equal to summability of the length operator associated with the growth graph. Using this, we compute spectral dimension of spheres. Communicated by Miriam Cohen.
Publication link
https://arxiv.org/pdf/1803.09407
URI
Subjects
46L87 | 58B32 | 58B34 | growth graph | homogeneous space | length operator | Spectral dimension