Compactness and Convergence in the Space of Analytic Functions

1973 ◽  
pp. 138-190
Author(s):  
John B. Conway
Keyword(s):  
Analytic Functions ◽  
Space Of Analytic Functions

scholarly journals The Multiplication Operator fromF(p,q,s)Spaces tonth Weighted-Type Spaces on the Unit Disk

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yongmin Liu ◽  
Yanyan Yu
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Multiplication Operator ◽  
Space Of Analytic Functions ◽  
Type Spaces ◽  
Weighted Type

LetH(𝔻)be the space of analytic functions on𝔻andu∈H(𝔻). The boundedness and compactness of the multiplication operatorMufromF(p,q,s),(or  F0(p,q,s))spaces tonth weighted-type spaces on the unit disk are investigated in this paper.

A special polynomial basis of a space of analytic functions

1988 ◽  
Vol 40 (1) ◽  
pp. 32-35
Author(s):  
V. I. Gorgula ◽  
N. I. Nagnibida
Keyword(s):  
Analytic Functions ◽  
Polynomial Basis ◽  
Space Of Analytic Functions ◽  
Special Polynomial

Growth of frequently hypercyclic functions for some weighted Taylor shifts on the unit disc

2020 ◽  
pp. 1-18
Author(s):  
Augustin Mouze ◽  
Vincent Munnier
Keyword(s):  
Critical Exponent ◽  
Analytic Functions ◽  
Unit Disc ◽  
Optimal Growth ◽  
Space Of Analytic Functions ◽  
Shift Operators ◽  
Image Position

Abstract For any $\alpha \in \mathbb {R},$ we consider the weighted Taylor shift operators $T_{\alpha }$ acting on the space of analytic functions in the unit disc given by $T_{\alpha }:H(\mathbb {D})\rightarrow H(\mathbb {D}),$ $ \begin{align*}f(z)=\sum_{k\geq 0}a_{k}z^{k}\mapsto T_{\alpha}(f)(z)=a_1+\sum_{k\geq 1}\Big(1+\frac{1}{k}\Big)^{\alpha}a_{k+1}z^{k}.\end{align*}$ We establish the optimal growth of frequently hypercyclic functions for $T_\alpha $ in terms of $L^p$ averages, $1\leq p\leq +\infty $ . This allows us to highlight a critical exponent.

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