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 ...

Network representation of protein structures is an information-rich mode of examining protein structure, dynamics and its interactions with biomolecules. Graph spectral methods are extremely useful and powerful in analysing ...

Grothendieck published an extraordinary paper entitled ”Resume de la theorie metrique des pro¬duits tensoriels topologiques” in 1953. The main result of this paper is the inequality which is commonly known as Grothendieck ...

This thesis consists of two broad themes. First one revolves around the Hardy's inequalities for the fractional power of Grushin operator $\G$ which is chased via two different approaches. In the first approach, we first ...

In this report, after recalling the definition of the M¨obius group, we define homogeneous operators, that is, operators T with the property '(T) is unitarily equivalent to T for all ' in the M¨obius group and prove some ...

Mathematical theory of homogenization of partial differential equations is relatively a new area of research (30-40 years or so) though the physical and engineering applications were well known. It has tremendous applications ...

Structural and functional annotation of sequences of putative proteins encoded in the newly sequenced genomes pose an important challenge. While much progress has been made towards high throughput experimental techniques ...

In the first chapter of this report, our aim is to introduce harmonic maps between Riemann surfaces using the Energy integral of a map. Once we have the desired prerequisites, we move on to show how to continuously deform ...

This work is concerned with two different problems in harmonic analysis, one on the Heisenberg group and other on Rn, as described in the following two paragraphs respectively. Let Hn be the (2n + 1)-dimensional Heisenberg ...