On the convergence of the Bieberbach polynomials in regions with piecewise analytic boundary

1992 ◽  
Vol 58 (5) ◽  
pp. 462-470 ◽  
Author(s):  
Dieter Gaier
Keyword(s):  
Analytic Boundary ◽  
Piecewise Analytic Boundary ◽  
Bieberbach Polynomials

scholarly journals On the Asymptotic Behavior of p-Faber Polynomials for Domains with Piecewise Analytic Boundary

2011 ◽  
Vol 2011 ◽  
pp. 1-8
Author(s):  
T. Tunc ◽  
M. Kucukaslan
Keyword(s):  
Asymptotic Behavior ◽  
Faber Polynomials ◽  
Geometric Properties ◽  
Analytic Boundary ◽  
Piecewise Analytic Boundary

Let be a domain bounded by a piecewise analytic Jordan's curve L, and let denote the p-Faber polynomials associated with G. We derive estimates of the form , for , where depends on geometric properties of L and the parameter p. Also, we show that O cannot be replaced by o in the relation given above.

On the Vector Sum of Two Convex Sets in Space

1991 ◽  
Vol 43 (2) ◽  
pp. 347-355 ◽  
Author(s):  
Steven G. Krantz ◽  
Harold R. Parks
Keyword(s):  
Convex Sets ◽  
Analytic Boundary ◽  
Real Analytic ◽  
Vector Sum ◽  
Bounded Convex

In the paper [KIS2], C. Kiselman studied the boundary smoothness of the vector sum of two smoothly bounded convex sets A and B in . He discovered the startling fact that even when A and B have real analytic boundary the set A + B need not have boundary smoothness exceeding C20/3 (this result is sharp). When A and B have C∞ boundaries, then the smoothness of the sum set breaks down at the level C5 (see [KIS2] for the various pathologies that arise).

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