Date Thesis Awarded

7-2012

Document Type

Honors Thesis

Degree Name

Bachelors of Science (BS)

Department

Mathematics

Advisor

Vladimir Bolotnikov

Committee Member

Jianjun Paul Tian

Committee Member

Ilya Spitkovsky

Committee Member

Joshua Gert

Abstract

The functions analytic in the upper half-plane and mapping the upper-half plane into itself (the so-called Pick functions) play a prominent role in several branches of mathematics. In this thesis we study fixed points of such functions. It is known that a Pick-class function different from the identity map can have at most one fixed point in the upper-half plane. However, it may have many (even infinitely many) appropriately defined boundary fixed points. We establish relations between the values of the derivative of a Pick function at these fixed points. Similar questions are considered in the context of Stieltjes-class functions which, in addition, are analytic on the positive half-axis and map this half-axis into itself.

Creative Commons License

Creative Commons License
This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Comments

Thesis is part of Honors ETD pilot project, 2008-2013. Migrated from Dspace in 2016.

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