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Riesz Transforms Associated With Heisenberg Groups And Grushin Operators
(2015-12-08)
We characterise the higher order Riesz transforms on the Heisenberg group and also show that they satisfy dimension-free bounds under some assumptions on the multipliers. We also prove the boundedness of the higher order ...
Infinitely Divisible Metrics, Curvature Inequalities And Curvature Formulae
(2014-06-30)
The curvature of a contraction T in the Cowen-Douglas class is bounded above by the
curvature of the backward shift operator. However, in general, an operator satisfying the curvature inequality need not be contractive. ...
Matchings Between Point Processes
(2014-06-20)
Fourier Analysis On Number Fields And The Global Zeta Functions
(2014-08-04)
The study of zeta functions is one of the primary aspects of modern number theory. Hecke was the first to prove that the Dedekind zeta function of any algebraic number field has an analytic continuation over the whole plane ...
Function Theory On Non-Compact Riemann Surfaces
(2014-06-30)
The theory of Riemann surfaces is quite old, consequently it is well developed. Riemann surfaces originated in complex analysis as a means of dealing with the problem of multi-valued functions. Such multi-valued functions ...
Ricci Flow And Isotropic Curvature
(2014-09-03)
This thesis consists of two parts. In the first part, we study certain Ricci flow invariant nonnegative curvature conditions as given by B. Wilking. We begin by proving that any such nonnegative curvature implies nonnegative ...
Analytic Continuation In Several Complex Variables
(2014-06-30)
We wish to study those domains in Cn,for n ≥ 2, the so-called domains of holomorphy, which are in some sense the maximal domains of existence of the holomorphic functions defined on them. We demonstrate that this study ...
Numerical Study Of Regularization Methods For Elliptic Cauchy Problems
(2011-06-30)
Cauchy problems for elliptic partial differential equations arise in many important applications, such as, cardiography, nondestructive testing, heat transfer, sonic boom produced by a maneuvering aerofoil, etc. Elliptic ...
The Caratheodory-Fejer Interpolation Problems and the Von-Neumann inequality
(2018-05-30)
The validity of the von-Neumann inequality for commuting $n$ - tuples of $3\times 3$ matrices remains open for $n\geq 3$. We give a partial answer to this question, which is used to obtain a necessary condition for the ...