Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/123715
Title: HERMITIAN POSITIVSTELLENSATZE AND INTEGRAL OPERATORS
Authors: TAN WEIYU, COLIN
Keywords: Hermitian, holomorphic, integral, isometry, manifold, positivity
Issue Date: 30-Nov-2015
Source: TAN WEIYU, COLIN (2015-11-30). HERMITIAN POSITIVSTELLENSATZE AND INTEGRAL OPERATORS. ScholarBank@NUS Repository.
Abstract: In this thesis, we consider positive Hermitian algebraic functions on holomorphic line bundles over compact complex manifolds. In particular, we consider the tensor product of certain positive powers of a positive Hermitian algebraic function satisfying the strong global Cauchy-Schwarz condition on a holomorphic line bundle with another fixed positive Hermitian algebraic function on another holomorphic line bundle. Our first main result is to give an effective estimate on the smallest power needed to be taken so that the integral operators associated to the resulting tensor product is a positive operator on the vector space of global holomorphic sections of the line bundle involved. The second main result is an effective Hermitan positivstellensatz. Namely, we give an effective estimate on the smallest power needed to be taken so that the resulting tensor product of Hermitian algebraic functions is a maximal sum of Hermitian squares.
URI: http://scholarbank.nus.edu.sg/handle/10635/123715
Appears in Collections:Ph.D Theses (Open)

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