Browsing Mathematics (MA) by Advisor "Bhattacharyya, Tirthankar"
Now showing items 1-10 of 10
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Dilation Theory of Contractions and Nevanlinna-Pick Interpolation Problem
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 ... -
Dilations, Functoinal Model And A Complete Unitary Invariant Of A r-contraction.
(2013-08-02)A pair of commuting bounded operators (S, P) for which the set r = {(z 1 +z 2,z 1z 2) : |z 1| ≤1, |z 2| ≤1} C2 is a spectral set, is called a r-contraction in the literature. For a contraction P and a bounded commutant ... -
Duality for Spaces of Holomorphic Functions into a Locally Convex Topological Vector Space
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 ... -
Interaction of distinguished varieties and the Nevanlinna-Pick interpolation problem in some domains
This thesis explores the interplay between complex geometry and operator theory, focusing on characterizing certain objects from algebraic geometry. Two concepts that have been of prime importance in recent times in the ... -
Invariants Associated with Complete Nevanlinna-Pick Spaces
The broad aim of this thesis is to study certain tuples of bounded operators that satisfy an operator inequality arising from a complete Nevanlinna-Pick kernel. Specifically, we focus on two invariants of these operator ... -
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 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 ... -
Operator Theory on Symmetrized Bidisc and Tetrablock-some Explicit Constructions
(2018-07-26)A pair of commuting bounded operators (S; P ) acting on a Hilbert space, is called a -contraction, if it has the symmetrised bides = f(z1 + z2; z1z2) : jz1j 1; jz2j 1g C2 as a spectral set. For every -contraction (S; P ), ... -
Some Problems in Multivariable Operator Theory
(2017-12-10)In this thesis we have investigated two different types of problems in multivariable operator theory. The first one deals with the defect sequence for contractive tuples and maximal con-tractive tuples. These condone deals ... -
Spectral Theory And Root Bases Associated With Multiparameter Eigenvalue Problems
(2010-06-01)Consider (1) -yn1+ q1y1 = (λr11 + µr12)y1 on [0, 1] y’1(0) = cot α1 and = y’1(1) = a1λ + b1 y1(0) y1(1) ...