2006/08/02 by Kristian P. Evans, Evans, Kristian P., Niels Jacob +1 · 1 citation
Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fractional Differential Equations Solutions #Functional Analysis (math.FA) #Mathematical functions and polynomials #math.FA
paper · pdf · doi:10.48550/arxiv.math/0608056
14 pages
openalex publication_date 2006/08/02 · arxiv created 2006/08/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For certain classes of negative definite symbols q(x,ξ) and state space dependent Bernstein function f(x,s) we prove that -p(x,D), the pseudo-differential operator with symbol -p(x,ξ)=-f(x,q(x,ξ)), extends to the generator of a Feller semigroup. Our result extends previously known results related to operators of variable (fractional) order of differentiation, or variable order fractional powers. New concrete examples are given.