Doctoral Dissertations

Abstract

"The purpose of this dissertation is to give an analytic disc approach to the CR extension problem. Analytic discs give a very convenient tool for holomorphic extension of CR functions. The type function is introduced and showed how these type functions have direct application to important questions about CR extension. In this dissertation the CR extension theorem is proved for a rigid hypersurface M in C2 given by y = (Re ω)m(Im ω)n where m and n are non-negative integers. If the type function is identically zero at the origin, then there is no CR extension. In such case the hypersurface is foliated by complex curves. If the type function is not identically zero at the origin, then CR function either locally extend to one or both sides of the hypersurface depending on the values of m and n. Finally using this result a more precise description of the extension set is given for CR functions defined on the hypersurface M"--Abstract, page iii.

Advisor(s)

Dwilewicz, Roman

Committee Member(s)

Harris, Adam
Grow, David E.
Le, Vy Khoi
Singler, John R.
Clark, Stephen L.

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Summer 2017

Pagination

viii, 52 pages

Note about bibliography

Includes bibliographic references (pages 50-51).

Rights

© 2017 Brijitta Antony, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 11472

Electronic OCLC #

1104294514

Download

Share

 
COinS