Journal article
Moment computations for graphs with fractal property
Journal of Applied Mathematics and Computing, Vol.37(1), pp.377-406
10/2011
DOI: 10.1007/s12190-010-0440-5
Abstract
In this paper, we use explicit formulas for the moments of a self-adjoint operator (radial operator), induced by a certain discrete structure, in Hilbert space. Our main theorem shows that the structures are classified by the moment computations producing an equivalence relation. Our motivation in turn derives from a groupoid-theoretic approach to spectral problems as they arise in quantum mechanics. While it is typically difficult to obtain explicit formulas for spectra, we demonstrate that our moment formulas serve as a substitute. The discrete structures $\Bbb{G}$ we study have a built in fractal feature: any portion of $\Bbb{G}$ is similar to the whole. And this fact (like in renormalization groups) serves to facilitate computations.
Details
- Title: Subtitle
- Moment computations for graphs with fractal property
- Creators
- Ilwoo Cho - Dep. of Math. St. Ambrose Univ. 421 Ambrose Hall, 518 W. Locust St. Davenport IA 52803 USAPalle Jorgensen - Dep. of Math. Univ. of Iowa 14 McLean Hall Iowa City IA 52242 USA
- Resource Type
- Journal article
- Publication Details
- Journal of Applied Mathematics and Computing, Vol.37(1), pp.377-406
- Publisher
- Springer-Verlag; Berlin/Heidelberg
- DOI
- 10.1007/s12190-010-0440-5
- ISSN
- 1598-5865
- eISSN
- 1865-2085
- Language
- English
- Date published
- 10/2011
- Academic Unit
- Mathematics
- Record Identifier
- 9983985994202771
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