Journal article
Monopoles, Dipoles, and Harmonic Functions on Bratteli Diagrams
Acta Applicandae Mathematicae, Vol.159(1), pp.169-224
02/15/2019
DOI: 10.1007/s10440-018-0189-7
Abstract
In our study of electrical networks we develop two themes: finding explicit formulas for special classes of functions defined on the vertices of a transient network, namely monopoles, dipoles, and harmonic functions. Secondly, our interest is focused on the properties of electrical networks supported on Bratteli diagrams. We show that the structure of Bratteli diagrams allows one to describe algorithmically harmonic functions as well as monopoles and dipoles. We also discuss some special classes of Bratteli diagrams (stationary, Pascal, trees), and we give conditions under which the harmonic functions defined on these diagrams have finite energy.
Details
- Title: Subtitle
- Monopoles, Dipoles, and Harmonic Functions on Bratteli Diagrams
- Creators
- Sergey Bezuglyi - 0000 0004 1936 8294 grid.214572.7 Department of Mathematics University of Iowa Iowa City 52242 IA USAPalle Jorgensen - 0000 0004 1936 8294 grid.214572.7 Department of Mathematics University of Iowa Iowa City 52242 IA USA
- Resource Type
- Journal article
- Publication Details
- Acta Applicandae Mathematicae, Vol.159(1), pp.169-224
- DOI
- 10.1007/s10440-018-0189-7
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- Publisher
- Springer Netherlands; Dordrecht
- Language
- English
- Date published
- 02/15/2019
- Academic Unit
- Mathematics
- Record Identifier
- 9983985821002771
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