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Trace Estimate For The Determinant Operator And K- Homogeneous Operators
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 ]\!\! ...
Homogenization of certain PDEs and associated optimal control problems on various rough domains
This thesis is devoted to the study of the asymptotic behavior of partial differential equations (PDEs) and associated boundary and interior optimal control problems in various oscillatory domains. The present thesis ...
Positivity preservers forbidden to operate on diagonal blocks
The question of which functions acting entrywise preserve positive semidefiniteness has
a long history, beginning with the Schur product theorem [Crelle 1911], which implies
that absolutely monotonic functions (i.e., ...
On certain invariant measures for correspondences, their analysis, and an application to recurrence
The aim of this dissertation is to analyse a certain class of dynamically interesting mea- sures arising in holomorphic dynamics that goes beyond the classical framework of maps. We study measures associated with semigroups ...
Hermitian Metrics and Singular Riemann Surface Foliations
The main aim of this thesis is to understand curvature properties of a given hermitian metric by restricting it to the leaves of a suitable singular Riemann surface foliation. We will specifically consider the complete ...
Structural connectivity correlates of human cognition explored with diffusion MRI and tractography
Intact structural connectivity among brain regions is critical to cognition. Structural connectivity forms the substratum for information flow between brain regions, and its plasticity is a hallmark of learning in the ...
Hardy's inequalities for Grushin operator and Hermite multipliers on Modulation spaces
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 ...
Finite Element Analysis of Optimal Control Problems Governed by Certain PDEs
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. ...
Semi-Markov Processes In Dynamic Games And Finance
(2010-07-01)
Two different sets of problems are addressed in this thesis. The first one is on partially observed semi-Markov Games (POSMG) and the second one is on semi-Markov modulated financial market model.
In this thesis we study ...
Orbit Model Analysis And Dynamic Filter Compensation For Onboard Autonomy
(2009-03-04)
Orbit of a spacecraft in three dimensional Inertial Reference Frame is in general represented by a standard set of six parameters like Keplerian Orbital Elements namely semimajor axis, eccentricity, inclination, ...