JournalsjfgVol. 3, No. 1pp. 75–93

Magnetic fields on resistance spaces

  • Michael Hinz

    Universität Bielefeld, Germany
  • Luke G. Rogers

    University of Connecticut, Storrs, USA
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On a metric measure space XX 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 XX. We provide sufficient conditions for closability and self-adjointness in terms of geometric conditions on the reference measure without assuming energy dominance.

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Michael Hinz, Luke G. Rogers, Magnetic fields on resistance spaces. J. Fractal Geom. 3 (2016), no. 1, pp. 75–93

DOI 10.4171/JFG/30