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Solution to a Bergman space extremal problem for non‐vanishing functions
Author(s) -
SheilSmall T.
Publication year - 2012
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/bds010
Subject(s) - mathematics , norm (philosophy) , bergman space , analytic function , bergman kernel , mathematical analysis , pure mathematics , space (punctuation) , linguistics , philosophy , political science , law , bounded function
For functions analytic and non‐vanishing in {| z |<1} and of the form f ( z )=1+ az + a 2 z 2 +…, with a ⩾0 given, we find the extremal function which minimizes the A 2 norm and calculate the exact minimum value of this norm.