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L2 Mergelyan Theorems in Several Complex Variables
Gubkin, Steven A

2015, Doctor of Philosophy, Ohio State University, Mathematics.
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.
Jeffery McNeal (Advisor)
James Fowler (Committee Member)
Kenneth Koenig (Committee Member)
78 p.

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Gubkin, S. (2015). L2 Mergelyan Theorems in Several Complex Variables. (Electronic Thesis or Dissertation). Retrieved from https://etd.ohiolink.edu/

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Gubkin, Steven. "L2 Mergelyan Theorems in Several Complex Variables." Electronic Thesis or Dissertation. Ohio State University, 2015. OhioLINK Electronic Theses and Dissertations Center. 23 Nov 2017.

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Gubkin, Steven "L2 Mergelyan Theorems in Several Complex Variables." Electronic Thesis or Dissertation. Ohio State University, 2015. https://etd.ohiolink.edu/

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