Some lower bound for holomorphic functions at the boundary

Some local definability theory for holomorphic functions

Let F be a collection of holomorphic functions and let R(PR(F)) denote the reduct of the structure Ran to the ordered field operations together with the set of proper restrictions (see below) of the real and imaginary parts of all functions in F . We ask the question: Which holomorphic functions are locally definable (ie have their real and imaginary parts locally definable) in the structure R(...

Lower Bound Functions for Polynomials

THE STEFAN PROBLEM WITH KINETIC FUNCTIONS AT THE FREE BOUNDARY

This paper considers a class of one-dimensional solidification problem in which kinetic undercooling is incorporated into the temperature condition at the interface. A model problem with nonlinear kinetic law is considered. The main result is an existence theorem. The mathematical effects of the kinetic term are discussed

Some notes on harmonic and holomorphic functions

These notes are concerned with harmonic and holomorphic functions on Euclidean spaces, where “holomorphic” refers to ordinary complex analysis in dimension 2 and generalizations using quaternions and Clifford algebras in higher dimensions. Among the principal themes are weak solutions, the mean-value property, and subharmonicity.

On the Boundary Values of Holomorphic Functions in Wedge Domains

WD = {z => x + iy\ x Q R , y & D). The distinguished boundary of WD is the set {z = x+iy \ xÇzR, y = 0 } , i.e., just R. In this paper we consider the following problem. Let ƒ be a real function on R satisfying certain regularity conditions. What are the conditions for the existence of a holomorphic function F on WD such that ƒ is the limit of Re -Fas the variable approaches the distinguished b...