Illinois Journal of Mathematics
- Illinois J. Math.
- Volume 52, Number 2 (2008), 347-363.
An areal analog of Mahler’s measure
We consider a version of height on polynomial spaces defined by the integral over the normalized area measure on the unit disk. This natural analog of Mahler’s measure arises in connection with extremal problems for Bergman spaces. It inherits many nice properties such as the multiplicative one. However, this height is a lower bound for Mahler’s measure, and it can be substantially lower. We discuss some similarities and differences between the two.
Illinois J. Math., Volume 52, Number 2 (2008), 347-363.
First available in Project Euclid: 23 July 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Pritsker, Igor E. An areal analog of Mahler’s measure. Illinois J. Math. 52 (2008), no. 2, 347--363. doi:10.1215/ijm/1248355339. https://projecteuclid.org/euclid.ijm/1248355339