Extremum problems relating to Bloch's and Landau's constants /
Variants of the classical Bloch's and Landau's constants are studied. Bounds are determined for the largest disc and largest schlicht disc that must be present in the image of a holomorphic function on the unit disc, normalized by the condition f(n)(0)=n!. The exact value of Bloch's (...
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| Format: | Thesis Book |
| Language: | English |
| Published: |
[Place of publication not identified] :
[publisher not identified] ;
2000.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=727720991&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Variants of the classical Bloch's and Landau's constants are studied. Bounds are determined for the largest disc and largest schlicht disc that must be present in the image of a holomorphic function on the unit disc, normalized by the condition f(n)(0)=n!. The exact value of Bloch's (= Landau's) constant is determined for holomorphic functions whose range is a) and annulus, b) a triangle, and c) a convex set. A numerical method is developed for computing Bloch's (= Landau's constant) ratio for covering maps. |
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| Item Description: | Vita. "Major Subject: Mathematics". |
| Physical Description: | viii, 82 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilm Inc. |
| Bibliography: | Includes bibliographical references (leaves 80-81). |