scholarly journals The Bernstein problem for affine maximal type hypersurfaces under decaying convexity

2020 ◽  
Vol 148 (6) ◽  
pp. 2631-2643
Author(s):  
Shi-Zhong Du
Keyword(s):  
Bernstein Problem

scholarly journals The Bernstein Problem in Dimension 6

1996 ◽  
Vol 185 (2) ◽  
pp. 420-439 ◽  
Author(s):  
J.Carlos Gutierrez Fernandez
Keyword(s):  
Bernstein Problem

scholarly journals Solution of the Bernstein Problem in the Non-regular Case

2000 ◽  
Vol 223 (1) ◽  
pp. 109-132 ◽  
Author(s):  
J.Carlos Gutiérrez Fernández
Keyword(s):  
Regular Case ◽  
Bernstein Problem

scholarly journals A Bernstein problem in warped products

2016 ◽  
Vol 41 ◽  
pp. 699-704
Author(s):  
Juan A. Aledo ◽  
Rafael M. Rubio
Keyword(s):  
Warped Products ◽  
Bernstein Problem

The Cauchy integral and analytic continuation

1985 ◽  
Vol 97 (3) ◽  
pp. 491-498 ◽  
Author(s):  
James. E. Brennan
Keyword(s):  
Analytic Continuation ◽  
Polynomial Approximation ◽  
Rational Functions ◽  
Minimum Problem ◽  
Weighted Polynomial Approximation ◽  
Cauchy Integral ◽  
Typical Problem ◽  
Bernstein Problem ◽  
Open Set ◽  
Simply Connected

One of the most important concepts in the theory of approximation by analytic functions is that of analytic continuation. In a typical problem, for example, there is generally a region Ω, a Banach space B of functions analytic in Ω and a subfamily ℱ ⊂ B, each member of which is analytic in some larger open set, and one might be asked to decide whether or not ℱ is dense in B. It often happens, however, that either ℱ is dense or the only functions which can be so approximated have a natural analytic continuation across ∂Ω. A similar phenomenon is also known to occur even for approximation on sets without interior. In this article we shall describe a method for proving such theorems which can be applied in a variety of settings and, in particular, to: (1)  the Bernštein problem for weighted polynomial approximation on the real line; (2)  the completeness problem for weighted polynomial approximation on bounded simply connected regions; (3) the Shapiro overconvergence problem for sequences of rational functions with sparse poles; (4) the Akutowicz-Carleson minimum problem for interpolating functions. Although we shall present no new results, the method of proof, which is based on an argument of the author [6], seems sufficiently versatile to warrant exposition.

scholarly journals The Bernstein problem for intrinsic graphs in Heisenberg groups and calibrations

2007 ◽  
Vol 30 (1) ◽  
pp. 17-49 ◽  
Author(s):  
Vittorio Barone Adesi ◽  
Francesco Serra Cassano ◽  
Davide Vittone
Keyword(s):  
Heisenberg Groups ◽  
Bernstein Problem
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