scholarly journals SOME NEW ESTIMATES FOR DISTANCES IN ANALYTIC FUNCTION SPACES OF SEVERAL COMPLEX VARIABLES AND DOUBLE BERGMAN REPRESENTATION FORMULA

2010 ◽  
Vol 03 (01) ◽  
pp. 48-54
Author(s):  
ROMI SHAMOYAN ◽  
MEHDI RADNIA
Keyword(s):  
Analytic Function ◽  
Representation Formula ◽  
Function Spaces ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Analytic Function Spaces

Linear forms in algebraic points of Abelian functions. II

1976 ◽  
Vol 79 (1) ◽  
pp. 55-70 ◽  
Author(s):  
D. W. Masser
Keyword(s):  
Analytic Function ◽  
Maximum Modulus ◽  
Complex Variables ◽  
Several Complex Variables ◽  
Maximum Modulus Principle ◽  
Linear Forms ◽  
Extrapolation Procedure ◽  
Abelian Functions

In this paper we continue to develop the apparatus needed for the proof of the theorem announced in (11). We retain the notation of (11) together with the assumptions made there about the field of Abelian functions. This section deals with properties of more general functions holomorphic on Cn. When n = 1 the extrapolation procedure in problems of transcendence is essentially the maximum modulus principle together with the act of dividing out zeros of an analytic function. For n > 1, however, this approach is not possible, and some mild theory of several complex variables is required. This was first used in the context of transcendence by Bombieri and Lang in (2) and (12), and we now give a brief account of the basic constructions of their papers.

scholarly journals Norm of a Volterra Integral Operator on Some Analytic Function Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Hao Li ◽  
Songxiao Li
Keyword(s):  
Analytic Function ◽  
Integral Operator ◽  
Unit Disc ◽  
Function Spaces ◽  
Volterra Integral Operator ◽  
Analytic Function Spaces

Let f be an analytic function in the unit disc 𝔻. The Volterra integral operator If is defined as follows: If(h)(z)=∫0zf(w)h'(w)dw,h∈H(𝔻),z∈𝔻. In this paper, we compute the norm of If on some analytic function spaces.

scholarly journals On composition operators inQKtype spaces

2007 ◽  
Vol 5 (2) ◽  
pp. 103-122 ◽  
Author(s):  
Marko Kotilainen
Keyword(s):  
Banach Space ◽  
Analytic Function ◽  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Function Spaces ◽  
Analytic Mapping ◽  
Analytic Function Spaces

Letp≥1,q>-2and letK:[0,∞)→[0,∞)be nondecreasing. With a different choice ofp,q,K, the Banach spaceQK(p,q)coincides with many well-known analytic function spaces. Boundedness and compactness of the composition operatorCφfromα-Bloch spaceBαintoQK(p,q)are characterized by a condition depending only on analytic mappingφ:𝔻→𝔻. The same properties are also studied in the caseCφ:QK(p,q)→Bα.

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