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math.CV2026
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…
math.CO2026
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…
math.CO2026
On formulas and fractional exponents for umbral operators
Kei Beauduin
We present a new formula for umbral operators that yields three main insights. First, it makes explicit a connection between umbral calculus and iteration theory. Second, it leads…