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Showing 1 to 14 of 14 for “"PARTIAL SUMS"”.
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Zeros of partial sums of power series
… on the unit circle is a limit point of zeros of partial sums of the power series. In this thesis, the relationship between the properties of the function and the behavior of the zeros of its partial sums is investigated. We prove that the set of limit points of xeros of partial sums of rational …
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Almost everywhere convergence of dyadic partial sums of Fourier series for almost periodic functions
… L\(^p\)(\(\char{bbold10}{0x54}\)), dyadic partial sums of the Fourier series of \(f\) converge almost everywhere for \(p\) \(\in\) (1, \(\infty\)). In 1968, E. A. Bredihina established an analogous result for the Stepanov spaces of almost periodic functions in the case \(p\) = 2. Here, a …
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Invariance Principles for Random Processes Generated by Extrema and Partial Sums of Random Variables
… well-known invariance principle of Strassen for partial sums. In our case, the strong invariance principle yields several weak convergence results for extremal processes. This differs from the case of partial sums in that Strassen's result does not yield the central limit theorem. By a similar …
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Ramanujan's identities, Voronoi summation formula, and zeros of partial sums of zeta and L-functions
Made available in DSpace on 2015-09-29T20:38:57Z (GMT). No. of bitstreams: 2 ROY-DISSERTATION-2015.pdf: 821854 bytes, checksum: 7abf6b7f9b1c512d8963ac66590c92b7 (MD5) LICENSE.txt: 4208 bytes, checksum: 502c6a39161a3e8620cd8507bf46885c (MD5) Previous issue date: 2015-08-03
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ΧΑΡΑΚΤΗΡΙΣΜΟΣ ΔΥΝΑΜΟΣΕΙΡΩΝ ΜΕ ΜΕΡΙΚΑ ΑΘΡΟΙΣΜΑΤΑ ΠΑΝΩ ΣΕ ΠΕΠΕΡΑΣΜΕΝΟ ΠΛΗΘΟΣ ΚΥΚΛΩΝ
… I.E. TAYLOR SERIES Σ C ZN FOR Z=E IX, WHOSE PARTIAL SUMS FOR ALL X IN E, WHERE E IS A NONDENUMERABLESUBSET OF (0,2Π) LIE ON A FINITE NUMBER OF CIRCLES (A PRIORI DEPENDINGON X) IN THE COMPLEX PLANE. THE MAIN RESULT OF THIS PAPER IS THAT FOR EVERY MEMBER OF THE CLASS K, THERE EXIST A COMPLEX …
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Pointwise and uniform convergence of fourier series on SU(2)
… unitary group SU (2). We prove that the Fourier partial sums of f converge to f uniformly on SU (2), thereby extending theorems of Caccioppoli, Mayer, and a special case of Ragozin. Pointwise convergence theorems for the Fourier series of functions on SU (2), due to Liu and Qian, were obtained by …
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Topics in Multiplicative and Probabilistic Number Theory
… the existing upper bounds on the maximum size of partial sums of odd order non-principal Dirichlet characters, both unconditionally and assuming the Generalized Riemann Hypothesis, and show that our conditional results are nearly best possible unconditionally. We also prove a quantitative …
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Lower bound techniques for data structures
… improved lower bounds for the following: * the partial-sums problem (a fundamental application of augmented binary search trees); * the predecessor problem (which is equivalent to IP lookup in Internet routers); * dynamic trees and dynamic connectivity; * orthogonal range stabbing. * orthogonal …
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Essays on Algorithmic Learning and Uncertainty Quantification
… uniform Gaussian approximation for partial sums in a reproducing kernel Hilbert space, which is then applied to construct uniform confidence bands for the widely-used kernel ridge regression algorithm. The third and final essay, titled “Frank-Wolfe Meets Metric Entropy,” uses ideas …
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Beatty ratios, algorithms related to Sturmian sequences and uniform distribution theory
… Sturmian sequence with slope $s$. We also study partial sums of the form \begin{equation} \label{thabs1} \sum_{n\leq x} \frac{ a_{n+k}}{a_n} \end{equation} and find asymptotics for them. Next, we consider the series \begin{equation*} \sum_{n=1}^{\infty} \left(\frac{ a_{n+k}}{a_n}-\frac{ …
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Visibility of lattice points in high dimensional spaces and extreme values of combinations of Dirichlet L-functions
… values of certain Dirichlet series and their partial sums. In particular, we examine a `short' partial sum of the Riemann Zeta function, $\zeta_N(s) = \sum_{n\le N}\frac{1}{n^s}$. We obtain large values of $\zeta_N\left(\frac{1}{2}+it\right)$ for $t\in[\sqrt{T}, T]$ when $N\le (\log …
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Martingale Convergence Techniques in Noncommutative Integration
… bounded weak type (1,1) estimate for the partial sums of the Fourier transform. This opens up classical problems from harmonic analysis in the noncommutative setting. The second problem we consider is the extension of the Komlos theorem to general finite von Neumann algebras. The Komlos …
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Studies of one-dimensional unimodal maps in the chaotic regime
… have been included, and the convergence of the partial sums of the measure is shown explicitly. It is conjectured that the asymptotic behavior of the partial sum of the measure as the number of levels goes to 00 is universal for the class of maps that have the same order of maximum. A new …