In a foundational paper “Operators Possesing an Open Set of Eigenvalues” written several decades ago, Cowen and Douglas showed that an operator T on a Hilbert space ‘H possessing an open set Ω C of eigenvalues determines ...

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 ...

Diffuse optical tomography (DOT) is one of the promising imaging modalities that pro- vides functional information of the soft biological tissues in-vivo, such as breast and brain tissues. The near infrared (NIR) light ...

In this article, we give two different proofs of the existence of the minimal isometric dilation of a single contraction. Then using the existence of a unitary dilation of a contraction, we prove the `von Neumann's ...

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 ...

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 ...

Let K be a compact subset of Cn . The polynomially convex hull of K is defined as The compact set K is said to be polynomially convex if = K. A closed subset is said to be locally polynomially convex at if there ...

The primary goal of this thesis is to study finite element based \textit{a priori} and \textit{a posteriori} error analysis of optimal control problems of various kinds governed by linear elliptic PDEs of second order. ...

In the first part of the talk we would discuss a topic about the Fourier coefficients of modular forms. Namely, we would focus on the question of distinguishing two modular forms by certain ‘arithmetically interesting’ ...