Skip to Main Content
Frequently Asked Questions
Submit an ETD
Global Search Box
Need Help?
Keyword Search
Participating Institutions
Advanced Search
School Logo
Files
File List
steven-gubkin-2015.pdf (849.05 KB)
ETD Abstract Container
Abstract Header
L
2
Mergelyan Theorems in Several Complex Variables
Author Info
Gubkin, Steven A
Permalink:
http://rave.ohiolink.edu/etdc/view?acc_num=osu1430998320
Abstract Details
Year and Degree
2015, Doctor of Philosophy, Ohio State University, Mathematics.
Abstract
An "approximation theorem" usually establishes the density of one space of functions in another, with respect to some norm. Classical examples include Runge's theorem and Mergelyan's theorem from single variable complex analysis. One analogue of Runge's theorem to several complex variables is the Oka-Weil Theorem. We offer an apparently new proof of this theorem which avoids a tricky duality argument. The main new theorems in the thesis are analogues of Mergelyan's theorem, only using L
2
instead of uniform norm approximations. In particular we show that if an open set U is strictly hyper convex, the space of holomorphic functions defined in a neighborhood of U is dense with respect to L
2
norm in the space of square integrable holomorphic functions defined on U. We then extend this result to L
2
approximation of dbar-closed (p,q)-forms.
Committee
Jeffery McNeal (Advisor)
James Fowler (Committee Member)
Kenneth Koenig (Committee Member)
Pages
78 p.
Subject Headings
Mathematics
Keywords
Several Complex Variables
;
approximation
;
Mergelyan
;
Runge
;
pseudoconvex
;
plurisubharmonic
;
holomorphic
Recommended Citations
Refworks
EndNote
RIS
Mendeley
Citations
Gubkin, S. A. (2015).
L
2
Mergelyan Theorems in Several Complex Variables
[Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1430998320
APA Style (7th edition)
Gubkin, Steven.
L
2
Mergelyan Theorems in Several Complex Variables.
2015. Ohio State University, Doctoral dissertation.
OhioLINK Electronic Theses and Dissertations Center
, http://rave.ohiolink.edu/etdc/view?acc_num=osu1430998320.
MLA Style (8th edition)
Gubkin, Steven. "L
2
Mergelyan Theorems in Several Complex Variables." Doctoral dissertation, Ohio State University, 2015. http://rave.ohiolink.edu/etdc/view?acc_num=osu1430998320
Chicago Manual of Style (17th edition)
Abstract Footer
Document number:
osu1430998320
Download Count:
1,441
Copyright Info
© 2015, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.