66 papers
This paper establishes sharp multidimensional Bohr radii for bounded holomorphic mappings on the unit polydisc by refining Bohr-type inequalities involving Schwarz functions and directional derivative operators, thereby generalizing univariate results to with rigorously verified optimality.
This paper presents a novel Lightning Method-based approach for solving the planar heat equation that combines Laplace transformation, Talbot inversion, and collocation to achieve spectral accuracy and robust performance across diverse geometric domains and time intervals.
The paper derives a single integral expression valid for all complex numbers that represents the reciprocal gamma function without requiring analytic continuation and simultaneously satisfies a specific functional identity involving the gamma function and sine.
This paper establishes a dimension-free Gehring-Hayman inequality for quasigeodesics in infinite-dimensional spaces by developing a new approach that relaxes previous constraints on geodesics and quasiconformal equivalence, thereby affirmatively resolving a long-standing open problem regarding the relationship between uniformity and Gromov hyperbolicity in Banach spaces.
This paper presents an algorithmic procedure combining Padé approximants and Borel-Écalle summation to construct rational approximations of functions with essential singularities, specifically applying the method to generate highly accurate tritronquée solutions and pole distributions for Painlevé's first equation.
This paper investigates the topological structure of Julia continua for disjoint-type transcendental entire functions, characterizing them as arc-like continua with span zero and demonstrating that a single such function can realize any arc-like continuum with a terminal point, while also resolving questions regarding accessibility from the Fatou set and the uniformity of escape to infinity.