Journal of Fractal Geometry

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Volume 3, Issue 1, 2016, pp. 75–93
DOI: 10.4171/JFG/30

Published online: 2016-05-09

Magnetic fields on resistance spaces

Michael Hinz[1] and Luke G. Rogers[2]

(1) Universit├Ąt Bielefeld, Germany
(2) University of Connecticut, Storrs, USA

On a metric measure space $X$ that supports a regular, strongly local resistance form we consider a magnetic energy form that corresponds to the magnetic Laplacian for a particle confined to $X$. We provide sufficient conditions for closability and self-adjointness in terms of geometric conditions on the reference measure without assuming energy dominance.

Keywords: Resistance forms, Dirichlet forms, magnetic Laplacians, self-adjointness

Hinz Michael, Rogers Luke: Magnetic fields on resistance spaces. J. Fractal Geom. 3 (2016), 75-93. doi: 10.4171/JFG/30