# A series representation of the discrete fractional Laplace operator of arbitrary order

@article{Jones2021ASR, title={A series representation of the discrete fractional Laplace operator of arbitrary order}, author={Tiffany Frug'e Jones and Evdokiya G. Kostadinova and Joshua Lee Padgett and Qin Sheng}, journal={ArXiv}, year={2021}, volume={abs/2101.03629} }

Abstract Although fractional powers of non-negative operators have received much attention in recent years, there is still little known about their behavior if real-valued exponents are greater than one. In this article, we define and study the discrete fractional Laplace operator of arbitrary real-valued positive order. A series representation of the discrete fractional Laplace operator for positive non-integer powers is developed. Its convergence to a series representation of a known case of… Expand

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