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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