Let $\Omega \subseteq \mathbb C^m$ be a bounded connected open set and $\mathcal H \subseteq \mathcal O(\Omega)$ be an analytic Hilbert module, i.e., the Hilbert space $\mathcal H$ possesses a reproducing kernel $K$, the ...

In this thesis we study questions broadly related to the Kobayashi (pseudo)distance and (pseudo)metric on domains in ℂn. Specifically, we study the following subjects: Estimates for holomorphic images of subsets in convex ...

Let ­½ Cm be a bounded domain and K :­£­!C be a sesqui-analytic function. We show that if ®,¯ È 0 be such that the functions K® and K¯, defined on ­£­, are non-negative definite kernels, then theMm(C) valued function ...

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 ...

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 ]\!\! ...

Consider an open subset O of the complex plane and a function f : O ÝÑ C. We understand the concept of holomorphicity of a complex-valued function. Suppose a function f defined on O takes values in a locally convex ...

This thesis is divided into four chapters. In Chapter 1, we give some basic definitions and results that we need throughout the thesis. In Chapter 2, we describe the pn0;n1q-Toom model and prove some known results about ...

Electrical signals from the brain can be recorded at several different scales, ranging from spiking activity to local field potential (LFP) in animals to scalp electroencephalogram (EEG) in humans. Each signal represents ...

Mycobacterium tuberculosis (M.tb), the causative agent of tuberculosis (TB), has remained the largest killer among infectious diseases for over a century. The increasing emergence of drug resistant varieties such as the ...

Proteins are essential for the growth, survival and maintenance of the cell. Understanding the functional roles of proteins helps to decipher the working of macromolecular assemblies and cellular machinery of living ...