5 papers
Repeated principal indefinite summation
Thomas Lamby, Jean-Luc Marichal
Under suitable asymptotic and convexity conditions on a function , the solution to , where is the forward difference operator, is uniq…
Rademacher's Theorem for Calderon-Zygmund-type Spaces
Thomas Lamby
Rademacher's Theorem can be interpreted as an almost-everywhere \emph{little- improvement principle}: if a function admits a uniform pointwise first-order Lipschitz control at e…
A Functorial Approach to Multi-Space Interpolation with Function Parameters
Thomas Lamby, Samuel Nicolay
We introduce an extension of interpolation theory to more than two spaces by employing a functional parameter, while retaining a fully functorial and systematic framework. This app…
The Thomae Function: Fractal Insights
Thomas Lamby, Samuel Nicolay
This article examines the Thomae function, a paradigmatic example of a function that is continuous on the irrationals and discontinuous elsewhere. Defined for a parameter , i…
Newton series representation of completely monotone functions
Thomas Lamby, Jean-Luc Marichal, Naïm Zenaïdi
We prove that every completely monotone function defined on a right-unbounded open interval admits a Newton series expansion at every point of that interval. This result can be vie…