# Browse Dissertations and Theses - Mathematics by Contributor "Boca, Florin"

• (2017-06-20)
We study the almost everywhere pointwise convergence of the solutions to Schrödinger equations in $\mathbb{R}^2$. It is shown that $\lim_{t \to 0} e^{it\Delta}f(x) = f(x)$ almost everywhere for all $f \in H^s (\mathbb{R}^2)$ ...

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• (2017-04-05)
This thesis explores three main topics in the application of ergodic theory and dynamical systems to equidistribution and spacing statistics in number theory. The first is concerned with utilizing the ergodic properties ...

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• (2017-04-06)
In the first part of this thesis, we will follow Kirchberg’s categorical perspective to establish new notions of WEP and QWEP relative to a C∗-algebra, and develop similar properties as in the classical WEP and QWEP. Also ...

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• (2014-09-16)
K.T. Atanassov introduced the two arithmetic functions $I(n) = \prod_{\nu=1}^k p_\nu^{1/\alpha_\nu} \qquad \text{and}\qquad R(n) = \prod_{\nu=1}^k p_\nu^{\alpha_v - 1}$ called the irrational factor and the strong ...

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• (2017-07-10)
This thesis is divided into two major topics. In the first, we study the topic of distribution of sequences modulo one. In particular, we look at the spacing distributions between members of rational valued sequences modulo ...

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• (2013-08-22)
In this thesis, we first study the correlations of some arithmetic sequences. We prove the existence of the limiting pair correlations of fractions with prime and power denominators, and give the explicit pair correlation ...

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• (2014-05-30)
In this work, we prove effective decay of certain multiple correlation coefficients for Weyl chamber actions of semidirect products of semisimple groups with $G$-vector spaces. Using these estimates we get decay for ...

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• (2013-05-24)
We improve the error term in the van der Corput transform for exponential sums, \sum g(n) exp(2 \pi i f(n)). For many smooth functions g and f, we can show that the largest factor of the error term is given by a simple ...

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• (2012-09-18)
The $q$-Gaussian von Neumann algebras were first defined and studied by Bo\.{z}ejko and Speicher in connection with noncommutative brownian motion. The main results of the present work is to establish that the $q$-Gaussian ...

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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)
Results from abstract harmonic analysis are extended to locally compact quantum groups by considering the noncommutative Lp-spaces associated with the locally compact quantum groups. Let G be a locally compact abelian ...

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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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• (2015-08-03)
The focus of the first part of the thesis commences with an examination of two pages in Ramanujan's lost notebook, pages 336 and 335. A casual, or even more prolonged, examination of the strange formulas on these pages ...

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• (2018-07-12)
In the first part of this thesis, we follow Varopoulos's perspective to establish the noncommutaive Sobolev inequaties (namely, Hardy-Littlewood-Sobolev inequalites), and extend the Sobolev embedding from noncommutative ...

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• (2018-07-11)
This thesis is divided into three major topics. In the first, we study questions concerning the distribution of lattice points in dimensions two and higher. We give asymptotic formulas for the number of integer lattice ...

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