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The Feller property for graphs


Author: Radosław K. Wojciechowski
Journal: Trans. Amer. Math. Soc. 369 (2017), 4415-4431
MSC (2010): Primary 39A12, 47B39, 60J27
DOI: https://doi.org/10.1090/tran/6901
Published electronically: January 9, 2017
MathSciNet review: 3624415
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Abstract: The Feller property concerns the preservation of the space of functions vanishing at infinity by the semigroup generated by an operator. We study this property in the case of the Laplacian on infinite graphs with arbitrary edge weights and vertex measures. In particular, we give conditions for the Feller property involving curvature-type quantities for general graphs, characterize the property in the case of model graphs and give some comparison results to the model case.


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Additional Information

Radosław K. Wojciechowski
Affiliation: Graduate Center of the City University of New York, 365 Fifth Avenue, New York, New York 10016 – and – York College of the City University of New York, 94-20 Guy R. Brewer Boulevard, Jamaica, New York 11451
Email: rwojciechowski@gc.cuny.edu

DOI: https://doi.org/10.1090/tran/6901
Received by editor(s): December 19, 2014
Received by editor(s) in revised form: January 8, 2016, and January 12, 2016
Published electronically: January 9, 2017
Additional Notes: The author gratefully acknowledges financial support from PSC-CUNY Awards, jointly funded by the Professional Staff Congress and the City University of New York, and the Collaboration Grant for Mathematicians, funded by the Simons Foundation.
Article copyright: © Copyright 2017 American Mathematical Society