scholarly journals Cone-volume measure and stability

2017 ◽  
Vol 306 ◽  
pp. 24-50 ◽  
Author(s):  
Károly J. Böröczky ◽  
Martin Henk
Keyword(s):  
Volume Measure

Feature Preserving Mesh Simplification Algorithm Based on Square Volume Measure

2009 ◽  
Vol 32 (2) ◽  
pp. 203-212 ◽  
Author(s):  
Yuan-Feng ZHOU ◽  
Cai-Ming ZHANG ◽  
Ping HE
Keyword(s):  
Mesh Simplification ◽  
Volume Measure ◽  
Feature Preserving

On Analytic Functions of Bergman BMO in the Ball

1999 ◽  
Vol 42 (1) ◽  
pp. 97-103 ◽  
Author(s):  
E. G. Kwon
Keyword(s):  
Hardy Space ◽  
Composition Operator ◽  
Analytic Functions ◽  
Bloch Space ◽  
Bounded Mean Oscillation ◽  
Open Unit ◽  
Bergman Metric ◽  
Open Unit Ball ◽  
Mean Oscillation ◽  
Volume Measure

AbstractLet B = Bn be the open unit ball of Cn with volume measure v, U = B1 and B be the Bloch space on , 1 ≤ α < 1, is defined as the set of holomorphic f : B → C for whichif 0 < α < 1 and , the Hardy space. Our objective of this note is to characterize, in terms of the Bergman distance, those holomorphic f : B → U for which the composition operator defined by , is bounded. Our result has a corollary that characterize the set of analytic functions of bounded mean oscillation with respect to the Bergman metric.

scholarly journals Commutants of Toeplitz operators on the ball and annulus

1995 ◽  
Vol 37 (3) ◽  
pp. 303-309 ◽  
Author(s):  
Željko Čučković ◽  
Dashan Fan
Keyword(s):  
Positive Integer ◽  
Bergman Space ◽  
Analytic Functions ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Volume Measure ◽  
Image Position

In this paper we study commutants of Toeplitz operators with polynomial symbols acting on Bergman spaces of various domains. For a positive integer n, let V denote the Lebesgue volume measure on ℂn. If ω is a domain in ℂn, then the Bergman space is defined to be the set of all analytic functions from ω into ℂ such that

scholarly journals Cone-volume measure of general centered convex bodies

2016 ◽  
Vol 286 ◽  
pp. 703-721 ◽  
Author(s):  
Károly J. Böröczky ◽  
Martin Henk
Keyword(s):  
Convex Bodies ◽  
Volume Measure

scholarly journals Isometries of a Bergman-Privalov-Type Space on the Unit Ball

2009 ◽  
Vol 2009 ◽  
pp. 1-16 ◽  
Author(s):  
Stevo Stević ◽  
Sei-Ichiro Ueki
Keyword(s):  
Unit Ball ◽  
Holomorphic Functions ◽  
Complete Characterization ◽  
Normalization Constant ◽  
Linear Isometry ◽  
Type Space ◽  
Basic Properties ◽  
Volume Measure ◽  
New Space

We introduce a new spaceANlog⁡,α(&#x1D539;)consisting of all holomorphic functions on the unit ball&#x1D539;⊂ℂnsuch that‖f‖ANlog⁡,α:=∫&#x1D539;φe(ln⁡(1+|f(z)|))dVα(z)<∞, whereα>−1,dVα(z)=cα,n(1−|z|2)αdV(z)(dV(z)is the normalized Lebesgue volume measure on&#x1D539;, andcα,nis a normalization constant, that is,Vα(&#x1D539;)=1), andφe(t)=tln⁡(e+t)fort∈[0,∞). Some basic properties of this space are presented. Among other results we proved thatANlog⁡,α(&#x1D539;)with the metricd(f,g)=‖f−g‖ANlog⁡,αis anF-algebra with respect to pointwise addition and multiplication. We also prove that every linear isometryTofANlog⁡,α(&#x1D539;)into itself has the formTf=c(f∘ψ)for somec∈ℂsuch that|c|=1and someψwhich is a holomorphic self-map of&#x1D539;satisfying a measure-preserving property with respect to the measuredVα. As a consequence of this result we obtain a complete characterization of all linear bijective isometries ofANlog⁡,α(&#x1D539;).

Area, Volume, Measure

Alfred Tarski ◽  
2014 ◽  
pp. 45-76
Author(s):  
Andrew McFarland ◽  
Joanna McFarland ◽  
James T. Smith
Keyword(s):  
Volume Measure
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