# Browse Dissertations and Theses - Mathematics by Contributor "Erdogan, M. Burak"

• (2016-08-25)
One of the widely studied topics in singular integral operators is T1 theorem. More precisely, it asks if one can extend a Calder\'on-Zygmund operator to a bounded operator on $L^p$. In addition, Tb theorem was raised when ...

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• (2012-09-18)
The thesis consists of six chapters. In Chapter 1, we will briefly introduce the background of the topic, as well as some results we already know. The next five chapters can be divided into two parts. The first part is ...

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• (2010)
Finally in Chapter 3 we consider a problem involving the non-linear Schrodinger equation. In particular, we consider the following equation that arises in fiber optic communication systems, iut+dtu xx+u2u=0. We can ...

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• (2010-08-31)
In this document we explore the issue of $L^1\to L^\infty$ estimates for the solution operator of the linear Schr\"{o}dinger equation, \begin{align*} iu_t-\Delta u+Vu&=0 &u(x,0)=f(x)\in \mathcal S(\R^n). \end{align*} We ...

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• (2011-08-25)
A Gabor system is a collection of modulated and translated copies of a window function. If we have a signal in $L^2(\mathbb{R})$, it can be analyzed with a Gabor system generated by a certain window $g$ and then synthesized ...

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• (2014-01-16)
This thesis is concerned with the restriction theory of the Fourier transform. We prove two restriction estimates for the Fourier transform. The first is a bilinear estimate for the light cone when the exponents are on a ...

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• (2018-06-22)
We first give a survey on multilinear Hilbert transforms. Then we study several variants of bilinear Hilbert transform such as bilinear Hilbert transform along two polynomials, discrete (integer) bilinear Hilbert transform ...

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• (2010-08-20)
There have been a lot of research done on the relationship between locally compact groups and algebras associated with them. For example, Johnson proved that a locally compact group G is amenable if and only if the ...

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• (2014-01-16)
In [20], Keith and Zhong prove that spaces admitting Poincar e inequalities also admit a priori stronger Poincar e inequalities. We use their technique, with slight adjustments, to obtain a similar result in the case of ...

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• (2014-05-30)
This dissertation consists of 4 chapters. In Chapter 1, we will briefly introduce some background of the trilinear oscillatory integrals and the motivations for their study. We also outline some key ideas in their proofs, ...

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• (2017-04-12)
This thesis is primarily concerned with the smoothing properties of dispersive equations and systems. Smoothing in this context means that the nonlinear part of the solution flow is of higher regularity than the initial ...

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• (2013-08-22)
In this dissertation we are interested in the study of dynamical systems that display rigidity and weak mixing. We are particularly interested in the topological analogue of rigidity, called uniform rigidity. A map $T$ ...

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