Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Spectral triples and wavelets for higher-rank graphs   In this paper, we present a new way to associate a finitely summable spectral
triple to a higher-rank graph $\Lambda$, via the infinite path space
$\Lambda^\infty$ of $\Lambda$. Moreover, we prove that this spectral triple has
a close connection to the wavelet decomposition of $\Lambda^\infty$ which was
introduced by Farsi, Gillaspy, Kang, and Packer in 2015. We first introduce the
concept of stationary $k$-Bratteli diagrams, in order to associate a family of
ultrametric Cantor sets, and their associated Pearson-Bellissard spectral
triples, to a finite, strongly connected higher-rank graph $\Lambda$. We then
study the zeta function, abscissa of convergence, and Dixmier trace associated
to the Pearson-Bellissard spectral triples of these Cantor sets, and show these
spectral triples are $\zeta$-regular in the sense of Pearson and Bellissard. We
obtain an integral formula for the Dixmier trace given by integration against a
measure $\mu$, and show that $\mu$ is a rescaled version of the measure $M$ on
$\Lambda^\infty$ which was introduced by an Huef, Laca, Raeburn, and Sims.
Finally, we investigate the eigenspaces of a family of Laplace-Beltrami
operators associated to the Dirichlet forms of the spectral triples. We show
that these eigenspaces refine the wavelet decomposition of $L^2(\Lambda^\infty,
M)$ which was constructed by Farsi et al.

18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex