# Analytic Function Theory

@inproceedings{Hille1959AnalyticFT,
title={Analytic Function Theory},
author={Einar Hille},
year={1959}
}
906 Citations
Radon Transform on spheres and generalized Bessel function associated with dihedral groups
Motivated by Dunkl operators theory, we consider a generating series involving a modified Bessel function and a Gegenbauer polynomial, that generalizes a known series already considered by L.Expand
On iterations of Misiurewicz's rational maps on the Riemann sphere
• Mathematics
• 1990
This paper concerns ergodic properties of rational maps of the Riemann sphere, of subexpanding behaviour. In particular we prove the existence of an absolutely continuous invariant measure, study itsExpand
Analytic Solutions of the Heat Equation
• Mathematics
• 2019
Motivated by the recent proof of Newman's conjecture \cite{R-T} we study certain properties of entire caloric functions, namely solutions of the heat equation $\partial_t F = \partial_z^2 F$ whichExpand
C V ] 5 J un 2 01 9 Analytic Solutions of the Heat Equation
Motivated by the recent proof of Newman’s conjecture [12] we study certain properties of entire caloric functions, namely solutions of the heat equation ∂tF = ∂ 2 zF which are entire in z and t. As aExpand
Linear functional equations with a catalytic variable and area limit laws for lattice paths and polygons
The technique combines the method of moments with the kernel method of algebraic combinatorics to find the joint distribution of signed areas and final altitude of a Brownian motion in terms of joint moments. Expand
A 2-variable power series approach to the Riemann hypothesis
We consider the power series in two complex variables By(fb)(x)=S_(n=0)|.A_n^b x^n y^(n(n+1)/2)., where .(-1).^n A_n^b are the non-zero coefficients of the Maclaurin series of the Riemann XiExpand
On a power series involving classical orthogonal polynomials
• Physics, Mathematics
• 2012
We investigate a class of power series occurring in some problems in quantum optics. Their coefficients are either Gegenbauer or Laguerre polynomials multiplied by binomial coefficients. AlthoughExpand
Limit laws for discrete excursions and meanders and linear functional equations with a catalytic variable
We study limit distributions for random variables defined in terms of coefficients of a power series which is determined by a certain linear functional equation. Our technique combines the method ofExpand
Spectral Asymptotics of Pauli Operators and Orthogonal Polynomials in Complex Domains
• Mathematics
• 2006
We consider the spectrum of a two-dimensional Pauli operator with a compactly supported electric potential and a variable magnetic field with a positive mean value. The rate of accumulation ofExpand
On the extension of the Painlevé property to difference equations
• Mathematics
• 2000
It is well known that the integrability (solvability) of a differential equation is related to the singularity structure of its solutions in the complex domain - an observation that lies behind theExpand