Global and local Goursat problems in a class of holomorphic or partially holomorphic functions
نویسندگان
چکیده
منابع مشابه
Global Holomorphic Functions in Several Noncommuting Variables
We define a free holomorphic function to be a function that is locally a bounded nc-function. We prove that free holomorphic functions are the functions that are locally uniformly approximable by free polynomials. We prove a realization formula and an OkaWeil theorem for free analytic functions.
متن کاملFrom Holomorphic Functions to Holomorphic Sections
It is a pleasure to have the opportunity in the graduate colloquium to introduce my research field. I am a differential geometer. To be more precise, I am a complex differential geometer, although I am equally interested in real differential geometry. To many people, geometry is a kind of mathematics that is related to length, area, volume, etc. For the Euclidean geometry, this is indeed the ca...
متن کاملSome 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(...
متن کاملMonotonicity and holomorphic functions
This is a survey on some recent works, mainly by the author on the relation between holomorphic functions on Kähler manifolds, monotonicity and the geometry of complex manifolds. We also use this opportunity to give details of a sketched step in the proof of a previously established result. Math Subject Classifications. Primary: 58G11, 53C44.
متن کاملProblems in Holomorphic Dynamics
Holomorphic dynamics posed several closely related key problems going back to Fatou and Julia: density of axiom A maps, local connectivity of the Julia and Mandelbrot sets, measure and dimension of the above sets. A great deal of progress has been achieved in these problems during the last decade, but they are still in the focus of modern reasearch. Most of the discussion in the chapter is conc...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 1981
ISSN: 0022-0396
DOI: 10.1016/0022-0396(81)90068-1