Browsing Mathematics (MA) by Subject "Research Subject Categories::MATHEMATICS"
Now showing items 21-37 of 37
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On certain invariant measures for correspondences, their analysis, and an application to recurrence
The aim of this dissertation is to analyse a certain class of dynamically interesting mea- sures arising in holomorphic dynamics that goes beyond the classical framework of maps. We study measures associated with semigroups ... -
On commuting isometries and commuting isometric semigroups
This thesis consists of two parts- commuting isometries and commuting isometric semigroups. In the first part, we study the Taylor joint spectrum for a pair of commuting isometries in certain cases. We show that the joint ... -
On existence and regularity of some complex Hessian equations on Kahler and transverse Kahler manifolds
The thesis consists of two parts. In the first part of the thesis, we classify the convergence behaviour of rotationally symmetric solutions to the modified J-flow on the blow-up of the complex projective space at a ... -
On regular subalgebras of symmetrizable Kac-Moody algebras and related combinatorics
In this thesis, we study two aspects of Kac-Moody algebras. One is to understand the subalgebras that can be embedded inside a Kac-Moody algebra as subalgebras generated by real root vectors. The other one is to explicitly ... -
On some canonical metrics on holomorphic vector bundles over Kahler manifolds
This thesis consists of two parts. In the first part, we introduce coupled Kähler- Einstein and Hermitian-Yang-Mills equations. It is shown that these equations have an interpretation in terms of a moment map. We identify ... -
On some structural problems in the theory of infinite-dimensional Lie (super)algebras
In this thesis, we examine two facets of infinite-dimensional Lie algebras. The first part focuses on the classification of $\pi$-systems in rank 2 Kac-Moody Lie algebras. In one of his seminal works, Dynkin classified the ... -
On the Geometry and Operator Theory of the Bidisc and the Symmetrized Bidisc
This work is concerned with the geometric and operator theoretic aspects of the bidisc and the symmetrized bidisc. First we have focused on the geometry of these two do- mains. The symmetrized bidisc, a non-homogeneous ... -
On two complex Hessian equations and convergence of corresponding flows
This thesis consists of three parts. Two important complex Hessian equations are studied on certain compact K\"ahler manifolds from different perspectives. The first one is the {\em J-equation} introduced independently by ... -
Positivity properties of the deformed Hermitian-Yang--Mills and related equations
In the first part of the talk, we briefly introduce the deformed Hermitian-Yang-Mills (dHYM) equation and discuss a result regarding the solvability of the twisted dHYM equation on compact Kähler three-folds with slightly ... -
Quasi-analytic Functions, Spherical Means, and Uncertainty Principles on Heisenberg Groups and Symmetric Spaces
This thesis has two parts. The first part revolves around certain theorems related to an uncertainty principle and quasi-analyticity. In contrast, the second part reflects a different mathematical theme, focusing on the ... -
Some Aspects of Weighted Kernel Functions on Planar Domains
The broad aim of this thesis is to study some aspects of weighted kernel functions. In particular, this thesis has been driven by three principal goals: First, to study the boundary behaviour of weighted Bergman kernels. ... -
Some dual realizations of Bergman and Hardy spaces on convex domains via integral transforms
The Fantappi{\`e} and Laplace transforms identify abstract spaces of analytic functionals with concrete function spaces, converting geometric support conditions into analytic growth conditions. Specifically, the space of ... -
Some results on beta ensembles and on scaling limits of random graphs
This thesis is divided into two main parts, each of which can be studied independently of the other. The first part is devoted to the study of beta ensembles (β-ensembles). The main theme in β-ensembles, in this thesis, ... -
A Study of Convergence, Quasi-Optimality, and Error Analysis of Adaptive Finite Element Methods for a class of PDEs
The central objective of this thesis is to carry out a rigorous analysis of finite element methods for second-order linear elliptic PDEs and for a variety of optimal control problems governed by second-order linear elliptic ... -
A Study of Some Conformal Metrics and Invariants on Planar Domains
The main aim of this thesis is to explain the behaviour of some conformal metrics and invariants near a smooth boundary point of a domain in the complex plane. We will be interested in the invariants associated to the ... -
Trace Estimate For The Determinant Operator And K- Homogeneous Operators
Let $\boldsymbol T=(T_1, \ldots , T_d)$ be a $d$- tuple of commuting operators on a Hilbert space $\mathcal H$. Assume that $\boldsymbol T$ is hyponormal, that is, $\big [\!\!\big [ \boldsymbol T^*, \boldsymbol T \big ]\!\! ... -
Weights of highest weight modules over Kac-Moody algebras
In this dissertation, broadly, we treat the weight-sets of arbitrary highest weight modules (uniformly) over all general complex Kac-Moody Lie algebras $\mathfrak{g}$, achieving the below. We obtain a uniform, explicit, ...