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Two applications of the Bergman spaces techniques
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
2010 (English)In: FIVE LECTURES IN COMPLEX ANALYSIS / [ed] Contreras MD; DiazMadrigal S, 2010, Vol. 525, 141-161 p.Conference paper (Refereed)
Abstract [en]

I am often asked by different people why the theory of Bergman spaces is so interesting that it attracts such an attention of researchers. My answer to this question is short: diversity makes theory so beautiful and interesting. First, it is diversity of methods used in the theory, sometimes coming from very unexpected areas of mathematics. Second, it is diversity of applications. The aim of this mini-course is to present two of such applications, one to an old problem in potential theory, the Hadamard conjecture on biharmonic Green functions, and another to estimates of conformal mappings. In both cases the results are obtained by an interplay of different techniques, Bergman spaces playing an important role.

These lectures cannot be considered as an introduction to the theory of Bergman spaces. Only those aspects of this theory which are needed for our applications will be touched upon. An interested reader is referred to recent books [21] and [9].

Place, publisher, year, edition, pages
2010. Vol. 525, 141-161 p.
, Contemporary Mathematics, ISSN 0271-4132 ; 525
URN: urn:nbn:se:kth:diva-29199ISI: 000283284500005OAI: diva2:393664
2nd Winter School Complex Analysis and Operator Theory, Univ Sevilla, Sevilla, SPAIN, FEB 05-09, 2008
QC 20110131Available from: 2011-01-31 Created: 2011-01-27 Last updated: 2011-01-31Bibliographically approved

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