etd@IISc Collection:http://etd.iisc.ernet.in/2005/412018-09-12T11:37:04Z2018-09-12T11:37:04ZWeighted Norm Inequalities for Weyl Multipliers and Hermite Pseudo-MultipliersBagchi, Sayanhttp://etd.iisc.ernet.in/2005/36412018-05-30T06:59:27Z2018-05-29T18:30:00ZTitle: Weighted Norm Inequalities for Weyl Multipliers and Hermite Pseudo-Multipliers
Authors: Bagchi, Sayan
Abstract: In this thesis we deal with two problems in harmonic analysis. In the ﬁrst problem we discuss weighted norm inequalities for Weyl multipliers satisfying Mauceri’s condition. As an application, we prove certain multiplier theorems on the Heisenberg group and also show in the context of a theorem of Weis on operator valued Fourier multipliers that the R-boundedness of the derivative of the multiplier is not necessary for the boundedness of the multiplier transform. In the second problem we deal with a variation of a theorem of Mauceri concerning the Lp bound-edness of operators Mwhich are known to be bounded on L2 .We obtain sufﬁcient conditions on the kernel of the operaor Mso that it satisﬁes weighted Lp estimates. As an application we prove Lp boundedness of Hermite pseudo-multipliers.2018-05-29T18:30:00ZVector Bundles Over Hypersurfaces Of Projective VarietiesTripathi, Amithttp://etd.iisc.ernet.in/2005/23182018-01-09T06:38:22Z2014-06-01T18:30:00ZTitle: Vector Bundles Over Hypersurfaces Of Projective Varieties
Authors: Tripathi, Amit
Abstract: In this thesis we study some questions related to vector bundles over hypersurfaces. More precisely, for hypersurfaces of dimension ≥ 2, we study the extension problem of vector bundles. We find some cohomological conditions under which a vector bundle over an ample divisor of non-singular projective variety, extends as a vector bundle to an open set containing that ample divisor.
Our method is to follow the general Groethendieck-Lefschetz theory by showing that a vector bundle extension exists over various thickenings of the ample divisor.
For vector bundles of rank > 1, we find two separate cohomological conditions on vector bundles which shows the extension to an open set containing the ample divisor. For the case of line bundles, our method unifies and recovers the generalized Noether-Lefschetz theorems by Joshi and Ravindra-Srinivas.
In the last part of the thesis, we make a specific study of vector bundles over elliptic curve.2014-06-01T18:30:00ZUnfolding Operators in Various Oscillatory Domains : Homogenization of Optimal Control ProblemsAiyappan, Shttp://etd.iisc.ernet.in/2005/36962018-06-13T07:46:45Z2018-06-12T18:30:00ZTitle: Unfolding Operators in Various Oscillatory Domains : Homogenization of Optimal Control Problems
Authors: Aiyappan, S
Abstract: In this thesis, we study homogenization of optimal control problems in various oscillatory domains. Specifically, we consider four types of domains given in Figure 1 below.
Figure 1: Oscillating Domains
The thesis is organized into six chapters. Chapter 1 provides an introduction to our work and the rest of the thesis. The main contributions of the thesis are contained in Chapters 2-5. Chapter 6 presents the conclusions of the thesis and possible further directions. A brief description of our work (Chapters 2-5) follows:
Chapter 2: Asymptotic behaviour of a fourth order boundary optimal control problem with Dirichlet boundary data posed on an oscillating domain as in Figure 1(A) is analyzed. We use the unfolding operator to study the asymptotic behavior of this problem.
Chapter 3: Homogenization of a time dependent interior optimal control problem on a branched structure domain as in Figure 1(B) is studied. Here we pose control on the oscillating interior part of the domain. The analysis is carried out by appropriately defined unfolding operators suitable for this domain. The optimal control is characterized using various unfolding operators defined at each branch of every level.
Chapter 4: A new unfolding operator is developed for a general oscillating domain as in Figure 1(C). Homogenization of a non-linear elliptic problem is studied using this new un-folding operator. Using this idea, homogenization of an optimal control problem on a circular oscillating domain as in Figure 1(D) is analyzed.
Chapter 5: Homogenization of a non-linear optimal control problem posed on a smooth oscillating domain as in Figure 1(C) is studied using the unfolding operator.2018-06-12T18:30:00ZUncertainty Handling In Knowledge-Based Systems Via Evidence RepresentationSrinivas, Nowdurihttp://etd.iisc.ernet.in/2005/18892018-01-09T06:27:00Z2013-01-17T18:30:00ZTitle: Uncertainty Handling In Knowledge-Based Systems Via Evidence Representation
Authors: Srinivas, Nowduri2013-01-17T18:30:00Z