Solution to a Bergman space extremal problem for non-vanishing functions (Q2903278)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Solution to a Bergman space extremal problem for non-vanishing functions |
scientific article; zbMATH DE number 6064199
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Solution to a Bergman space extremal problem for non-vanishing functions |
scientific article; zbMATH DE number 6064199 |
Statements
Solution to a Bergman space extremal problem for non-vanishing functions (English)
0 references
8 August 2012
0 references
harmonic product
0 references
extremal problems
0 references
minimize area problems for nonvanishing functions
0 references
The author gives an impressive solution to an open problem in function theory. Let \(f(z)= 1+ az+ a_2 z^2+\cdots\) with \(a\geq 0\) be analytic in \(\{|z|< 1\}\). A long standing open problem was to fiind an extremal function solution that minimizes the \(A^2\) norm, and to find, in addition, the exact value of this minimum norm. The author uses his theory of harmonic products as a basic tool. He gives a beautiful solution.
0 references
