Advanced search options

Advanced Search Options 🞨

Browse by author name (“Author name starts with…”).

Find ETDs with:

in
/  
in
/  
in
/  
in

Written in Published in Earliest date Latest date

Sorted by

Results per page:

Sorted by: relevance · author · university · dateNew search

You searched for subject:( Mergelyan). Showing records 1 – 3 of 3 total matches.

Search Limiters

Last 2 Years | English Only

No search limiters apply to these results.

▼ Search Limiters

1. Gubkin, Steven A. L2 Mergelyan Theorems in Several Complex Variables.

Degree: PhD, Mathematics, 2015, The Ohio State University

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 L2 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 L2 norm in the space of square integrable holomorphic functions defined on U. We then extend this result to L2 approximation of dbar-closed (p,q)-forms. Advisors/Committee Members: McNeal, Jeffery (Advisor).

Subjects/Keywords: Mathematics; Several Complex Variables; approximation; Mergelyan; Runge; pseudoconvex; plurisubharmonic; holomorphic

…CHAPTER 1 INTRODUCTION 1.1 Runge vs. Mergelyan In one complex variable, two major… …Theorem 1.1.2 (Mergelyan). If K is a compact subset of C and f is both continuous on K… …Modified Mergelyan). If K is a compact subset of C and f is both continuous on K and… …Modified Mergelyan theorem and the “regular” Mergelyan theorem is that in the modified version we… …work we prove several L2 “Mergelyan type” theorems, which model themselves on the Modified… 

Page 1 Page 2 Page 3 Page 4 Page 5 Page 6 Page 7

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Gubkin, S. A. (2015). L2 Mergelyan Theorems in Several Complex Variables. (Doctoral Dissertation). The Ohio State University. Retrieved from http://rave.ohiolink.edu/etdc/view?acc_num=osu1430998320

Chicago Manual of Style (16th Edition):

Gubkin, Steven A. “L2 Mergelyan Theorems in Several Complex Variables.” 2015. Doctoral Dissertation, The Ohio State University. Accessed October 25, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=osu1430998320.

MLA Handbook (7th Edition):

Gubkin, Steven A. “L2 Mergelyan Theorems in Several Complex Variables.” 2015. Web. 25 Oct 2020.

Vancouver:

Gubkin SA. L2 Mergelyan Theorems in Several Complex Variables. [Internet] [Doctoral dissertation]. The Ohio State University; 2015. [cited 2020 Oct 25]. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1430998320.

Council of Science Editors:

Gubkin SA. L2 Mergelyan Theorems in Several Complex Variables. [Doctoral Dissertation]. The Ohio State University; 2015. Available from: http://rave.ohiolink.edu/etdc/view?acc_num=osu1430998320


University of Vienna

2. Reiter, Michael. Approximation of CR functions.

Degree: 2009, University of Vienna

In dieser Arbeit werden wir einige Approximationsresultate in der Komplexen Analysis diskutieren. Beginnend mit den klassischen Sätzen von Runge und Mergelyan wird hauptsächlich Approximation von CR Funktionen auf CR Teilmannigfaltigkeiten des ℂn durch ganze Funktionen behandelt. Diese verallgemeinerten holomorphen Funktionen auf CR Teilmannigfaltigkeiten können lokal immer durch ganze Funktionen approximiert werden, was mit dem Satz von Baouendi-Treves bewiesen wird. Neuere Arbeiten untersuchen globale Approximation von CR Funktionen. Hier werden wir den Fall einer Hyperfläche und die Situation in höheren Kodimensionen betrachten.

In this present work we are going to discuss several approximation results in Complex Analysis. Starting with the classical approximation theorems by Runge and Mergelyan we mainly investigate approximation of CR functions on CR submanifolds in ℂn by entire functions. These generalized versions of holomorphic functions on CR submanifolds can always be approximated locally on CR submanifolds by entire functions. This result is covered by the Baouendi-Treves-Approximation Theorem. More recent works treat global approximation of CR functions. We will present the hypersurface case and discuss the situation in higher codimensions.

Subjects/Keywords: 31.43 Funktionen mit mehreren komplexen Variablen; 31.42 Funktionen mit einer komplexen Variablen; CR Funktionen / CR Teilmannigfaltigkeit / globale Approximation / Runge / Mergelyan / Baouendi-Treves-Approximationssatz; CR functions / CR submanifolds / global approximation / Runge / Mergelyan / Baouendi-Treves-Approximation Theorem

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Reiter, M. (2009). Approximation of CR functions. (Thesis). University of Vienna. Retrieved from http://othes.univie.ac.at/7113/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Reiter, Michael. “Approximation of CR functions.” 2009. Thesis, University of Vienna. Accessed October 25, 2020. http://othes.univie.ac.at/7113/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Reiter, Michael. “Approximation of CR functions.” 2009. Web. 25 Oct 2020.

Vancouver:

Reiter M. Approximation of CR functions. [Internet] [Thesis]. University of Vienna; 2009. [cited 2020 Oct 25]. Available from: http://othes.univie.ac.at/7113/.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Reiter M. Approximation of CR functions. [Thesis]. University of Vienna; 2009. Available from: http://othes.univie.ac.at/7113/

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

3. Τσιρίβας, Νικόλαος. Καθολικές σειρές και συναρτήσεις και υπερκυκλικότητα.

Degree: 2008, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ)

Subjects/Keywords: Καθολικές σειρές; Καθολικές συναρτήσεις; Υπερκυκλικοί τελεστές; Θεώρημα κατηγορίας Baire; Θεώρημα Roung; Θεώρημα Mergelyan; Σειρές Faber; Σειρές Taylor; Universal series; Universal functions; Ypercyclic operators; Baire's category theorem; Runge's theorem; Mergelyan's theorem; Faber series; Taylor series

Record DetailsSimilar RecordsGoogle PlusoneFacebookTwitterCiteULikeMendeleyreddit

APA · Chicago · MLA · Vancouver · CSE | Export to Zotero / EndNote / Reference Manager

APA (6th Edition):

Τσιρίβας, . . (2008). Καθολικές σειρές και συναρτήσεις και υπερκυκλικότητα. (Thesis). National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Retrieved from http://hdl.handle.net/10442/hedi/24113

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Chicago Manual of Style (16th Edition):

Τσιρίβας, Νικόλαος. “Καθολικές σειρές και συναρτήσεις και υπερκυκλικότητα.” 2008. Thesis, National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ). Accessed October 25, 2020. http://hdl.handle.net/10442/hedi/24113.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

MLA Handbook (7th Edition):

Τσιρίβας, Νικόλαος. “Καθολικές σειρές και συναρτήσεις και υπερκυκλικότητα.” 2008. Web. 25 Oct 2020.

Vancouver:

Τσιρίβας . Καθολικές σειρές και συναρτήσεις και υπερκυκλικότητα. [Internet] [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2008. [cited 2020 Oct 25]. Available from: http://hdl.handle.net/10442/hedi/24113.

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

Council of Science Editors:

Τσιρίβας . Καθολικές σειρές και συναρτήσεις και υπερκυκλικότητα. [Thesis]. National and Kapodistrian University of Athens; Εθνικό και Καποδιστριακό Πανεπιστήμιο Αθηνών (ΕΚΠΑ); 2008. Available from: http://hdl.handle.net/10442/hedi/24113

Note: this citation may be lacking information needed for this citation format:
Not specified: Masters Thesis or Doctoral Dissertation

.