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Restricted Isometric Projections For Differentiable Manifolds And Applications, Vasile Pop
Restricted Isometric Projections For Differentiable Manifolds And Applications, Vasile Pop
USF Tampa Graduate Theses and Dissertations
The restricted isometry property (RIP) is at the center of important developments in compressive sensing. In RN, RIP establishes the success of sparse recovery via basis pursuit for measurement matrices with small restricted isometry constants δ2s < 1=3. A weaker condition, δ2s < 0:6246, is actually sufficient to guarantee stable and robust recovery of all s-sparse vectors via l1-minimization. In infinite Hilbert spaces, a random linear map satisfies a general RIP with high probability and allow recovering and extending many known compressive sampling results. This thesis extends the known restricted isometric projection of sparse datasets of vectors embedded in the Euclidean spaces RN down into low-dimensional subspaces Rm ,m << N …
Orthogonal Polynomials With Respect To The Measure Supported Over The Whole Complex Plane, Meng Yang
Orthogonal Polynomials With Respect To The Measure Supported Over The Whole Complex Plane, Meng Yang
USF Tampa Graduate Theses and Dissertations
In chapter 1, we present some background knowledge about random matrices, Coulomb gas, orthogonal polynomials, asymptotics of planar orthogonal polynomials and the Riemann-Hilbert problem. In chapter 2, we consider the monic orthogonal polynomials, $\{P_{n,N}(z)\}_{n=0,1,\cdots},$ that satisfy the orthogonality condition,
\begin{equation}\nonumber \int_\mathbb{C}P_{n,N}(z)\overline{P_{m,N}(z)}e^{-N Q(z)}dA(z)=h_{n,N}\delta_{nm} \quad(n,m=0,1,2,\cdots), \end{equation}
where $h_{n,N}$ is a (positive) norming constant and the external potential is given by
$$Q(z)=|z|^2+ \frac{2c}{N}\log \frac{1}{|z-a|},\quad c>-1,\quad a>0.$$
The orthogonal polynomial is related to the interacting Coulomb particles with charge $+1$ for each, in the presence of an extra particle with charge $+c$ at $a.$ For $N$ large and a fixed ``c'' this …