2021/01/10 by Tiffany Frugé Jones, Jones, Tiffany Frugé, Evdokiya Kostadinova +4 · 2 citations
Mathematics · #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical Inequalities and Applications #Mathematical functions and polynomials #Numerical Analysis (math.NA) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2101.03629
openalex publication_date 2021/01/10 · openalex created_date 2021/01/18 · openalex updated_date 2026/07/28
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 positive integer powers is proven as the power tends to the integer value. Furthermore, we show that the new representation for arbitrary real-valued positive powers of the discrete Laplace operator is consistent with existing theoretical results.