Laurent series of holomorphic functions smooth up to the boundary
نویسندگان
چکیده
It is shown that the Laurent series of a holomorphic function smooth up to boundary on Reinhardt domain in $${\mathbb {C}}^n$$ converges unconditionally Fréchet topology space functions boundary.
منابع مشابه
Modeling Potential Flow Using Laurent Series Expansions and Boundary Elements
The fundamental underpinnings of the well-known Bernoulli’s Equation, as used to describe steady state two-dimensional flow of an ideal incompressible irrotational flow, are typically described in terms of partial differential equations. However, it has been shown that the Cauchy Integral Theorem of standard complex variables also explain the Bernoulli’s Equation and, hence, can be directly use...
متن کاملOn 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...
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 کاملRadar Ambiguity Functions, the Heisenberg Group, and Holomorphic Theta Series
The concept of linear Schrödinger representation of the real Heisenberg nilpotent group and its various realizations is used to link the theory of radar ambiguity functions with nilpotent harmonic analysis. This group-representation theoretic approach allows us to analyze the radar ambiguity functions simultaneously in time and frequency. Moreover, it allows us to determine the group of all tra...
متن کاملBoundary Values of Bounded Holomorphic Functions of Several Variables
A typical result (consequence of Theorem 1) is that if such a function tends to a limit X as x—»x° from inside an open cone with vertex at x°, then it tends "on the average" to X as x—>x° from inside any open cone with vertex at x°. In particular, if such a function tends to limits in each of two open cones with a common vertex, these limits must be equal; for n = l (when the cones are half-lin...
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: Complex analysis and its synergies
سال: 2021
ISSN: ['2197-120X', '2524-7581']
DOI: https://doi.org/10.1007/s40627-021-00080-1