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Laurent series of holomorphic functions smooth up to the boundary

143   0   0.0 ( 0 )
 Added by Anirban Dawn
 Publication date 2020
  fields
and research's language is English
 Authors Anirban Dawn




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It is shown that the Laurent series of a holomorphic function smooth up to the boundary on a Reinhardt domain in $mathbb{C}^n$ converges unconditionally to the function in the Fr{e}chet topology of the space of functions smooth up to the boundary.



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102 - Matt Hohertz 2021
Kalantaris Geometric Modulus Principle describes the local behavior of the modulus of a polynomial. Specifically, if $p(z) = a_0 + sum_{j=k}^n a_jleft(z-z_0right)^j,;a_0a_ka_n eq 0$, then the complex plane near $z = z_0$ comprises $2k$ sectors of angle $frac{pi}{k}$, alternating between arguments of ascent (angles $theta$ where $|p(z_0 + te^{itheta})| > |p(z_0)|$ for small $t$) and arguments of descent (where the opposite inequality holds). In this paper, we generalize the Geometric Modulus Principle to holomorphic and harmonic functions. As in Kalantaris original paper, we use these extensions to give succinct, elegant new proofs of some classical theorems from analysis.
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83 - Qian Guan 2018
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