4 papers · 1 filter
Meromorphic order from Taylor coefficients, least singular values of Hankel matrices and rational approximants
Kei Beauduin
We introduce a natural notion of generalized order for entire and meromorphic functions and express it in terms of their Taylor coefficients. More precisely, one formula uses the l…
When can a power series be analytically continued?
Kei Beauduin
A classical line of research characterizes analytic continuation of power series through analytic interpolation of their coefficients. Under suitable hypotheses, the growth of the…
The indicator diagram theory for maximal type entire functions and the characterization of analytic continuability
Kei Beauduin
We extend Pólya's indicator diagram theory to encompass entire functions of order at most 1, allowing functions of maximal type. To do so, we introduce an extension of the complex…
A general identity for umbral operators and a special subclass
Kei Beauduin
We prove a new universal identity for umbral operators. This motivates the definition of a subclass satisfying a simplified identity, which we fully characterize. The results are i…