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Dynamical Properties of Families of Holomorphic Mappings
(2018-06-08)
Thesis Abstract
In the first part of the thesis, we study some dynamical properties of skew products of H´enon maps of C2 that are fibered over a compact metric space M . The problem reduces to understanding the dynamical ...
Betti Numbers, Grobner Basis And Syzygies For Certain Affine Monomial Curves
(Indian Institute of Science, 2007-03-30)
Let e > 3 and mo,... ,me_i be positive integers with gcd(m0,... ,me_i) = 1, which form an almost arithmetic sequence, i.e., some e - 1 of these form an arithmetic progression. We further assume that m0,... ,mc_1 generate ...
Some Descriptions Of The Envelopes Of Holomorphy Of Domains in Cn
(2011-08-09)
It is well known that there exist domains Ω in Cn,n ≥ 2, such that all holomorphic functions in Ω continue analytically beyond the boundary. We wish to study this remarkable phenomenon. The first chapter seeks to motivate ...
The Green's Function, the Bergman Kernel and Quadrature Domains in Cn
(2018-06-08)
In the first part of this thesis, we prove two density theorems for quadrature domains in Cn ,n≥2. It is shown that quadrature domains are dense in the class of all product domains of the form D×Ωwhere D⊂Cn−1 is a smoothly ...
Bounded Analytic Functions On The Unit Disc
(2011-08-09)
In this thesis, we have dealt primarily with two function algebras. The first one is the space of all holomorphic functions on the unit disc D in the complex plane which are continuous up to the boundary, denoted by A(D). ...
Rigidity And Regularity Of Holomorphic Mappings
(2015-07-16)
We deal with two themes that are illustrative of the rigidity and regularity of holomorphic
mappings.
The first one concerns the regularity of continuous CR mappings between smooth pseudo convex, finite type hypersurfaces ...
Riesz Transforms Associated With Heisenberg Groups And Grushin Operators
(2015-12-08)
We characterise the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order ...
Matchings Between Point Processes
(2014-06-20)
Analytic Continuation In Several Complex Variables
(2014-06-30)
We wish to study those domains in Cn,for n ≥ 2, the so-called domains of holomorphy, which are in some sense the maximal domains of existence of the holomorphic functions defined on them. We demonstrate that this study ...
The Caratheodory-Fejer Interpolation Problems and the Von-Neumann inequality
(2018-05-30)
The validity of the von-Neumann inequality for commuting $n$ - tuples of $3\times 3$ matrices remains open for $n\geq 3$. We give a partial answer to this question, which is used to obtain a necessary condition for the ...