dc.contributor.author |
Maziad, Fatima Moussa, |
dc.date |
2014 |
dc.date.accessioned |
2015-02-03T10:43:36Z |
dc.date.available |
2015-02-03T10:43:36Z |
dc.date.issued |
2014 |
dc.date.submitted |
2014 |
dc.identifier.other |
b18265005 |
dc.identifier.uri |
http://hdl.handle.net/10938/10228 |
dc.description |
Thesis. M.S. American University of Beirut. Department of Mathematics, 2014. T:6040 |
dc.description |
Advisor : Dr. Faruk Abi-Khuzam, Professor, Mathematics ; Members of Committee : Dr. Bassam Shayya, Professor, Mathematics ; Dr. Tamer Tlas, Assistant Professor, Mathematics. |
dc.description |
Includes bibliographical references (leaf 51) |
dc.description.abstract |
The Bergman space A2 consists of functions analytic and square integrable on a region of the complex plane. The Berezina transform T of a function in this space is defined as the Berezin transform of the Toeplitz operator. A question of interest is to determine fixed points of the Berezin transform. In this thesis, we present a partial study of work done on this question. We first consider the case where the region is the open unit disk D and present conditions for which Tu≤ u and Tu≥ u, where u is integrable. We then consider the more difficult case where the region is an annulus centered at the origin. In the case of a radial function, we present conditions implying either Tu ≥u, or Tu≤u. |
dc.format.extent |
1 online resource (vi, 51 leaves) ; 30cm |
dc.language.iso |
eng |
dc.relation.ispartof |
Theses, Dissertations, and Projects |
dc.subject.classification |
T:006040 AUBNO |
dc.subject.lcsh |
Functions of complex variables. |
dc.subject.lcsh |
Fixed point theory. |
dc.subject.lcsh |
Bergman spaces. |
dc.subject.lcsh |
Mathematical analysis. |
dc.title |
On the fixed points of the Berezin transform - |
dc.type |
Thesis |
dc.contributor.department |
American University of Beirut. Faculty of Arts and Sciences. Department of Mathematics, degree granting institution. |