3 papers
math.FA2026
On the Unique Continuation Principle for a Class of Translation Invariant Nonlocal Operators
David Berger, Rene L. Schilling
The unique continuation property (UCP) for an operator says that, if holds on an open set , then one has everywhere. We establish necessary and sufficient…
math.PR2025
Bernstein Fractional Derivatives: Censoring and Stochastic Processes
David Berger, Cailing Li, René L. Schilling
We define censored fractional Bernstein derivatives on the positive half-line based on the Bernstein--Riemann--Liouville fractional derivative. The censored fractional derivative t…
math.AP2024
An extension of the Liouville theorem for Fourier multipliers to sub-exponentially growing solutions
David Berger, René L. Schilling, Eugene Shargorodsky +1
We study the equation in a large class of sub-exponentially growing functions. Under appropriate restrictions on , we show that every such soluti…