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1	On the reconstruction of multivariate exponential sums von der Ohe, Ulrich 07 December 2017 (has links) We develop a theory concerning the reconstruction of multivariate exponential sums first over arbitrary fields and then consider the special cases of multivariate exponential sums over the fields of real and complex numbers. exponential sum reconstruction Prony's method multivariate ddc:510
2	Topics in Analytic Number Theory Powell, Kevin James 31 March 2009 (has links) (PDF) The thesis is in two parts. The first part is the paper “The Distribution of k-free integers” that my advisor, Dr. Roger Baker, and I submitted in February 2009. The reader will note that I have inserted additional commentary and explanations which appear in smaller text. Dr. Baker and I improved the asymptotic formula for the number of k-free integers less than x by taking advantage of exponential sum techniques developed since the 1980's. Both of us made substantial contributions to the paper. I discovered the exponent in the error term for the cases k=3,4, and worked the case k=3 completely. Dr. Baker corrected my work for k=4 and proved the result for k=5. He then generalized our work into the paper as it now stands. We also discussed and both contributed to parts of section 3 on bounds for exponential sums. The second part represents my own work guided by my advisor. I study the zeros of derivatives of Dirichlet L-functions. The first theorem gives an analog for a result of Speiser on the zeros of ζ'(s). He proved that RH is equivalent to the hypothesis that ζ'(s) has no zeros with real part strictly between 0 and ½. The last two theorems discuss zero-free regions to the left and right for L^{(k)}(s,χ). Derivative Dirichlet L-function k-free integer exponential sum Heath-Brown Decomposition Zeros Zero-free region left right Generalized Riemann Hypothesis GRH r-free integers Equivalence Type I sum Type II sum Asymptotic formula Mathematics
3	Parameter estimation for nonincreasing exponential sums by Prony-like methods Potts, Daniel, Tasche, Manfred 02 May 2012 (has links) (PDF) For noiseless sampled data, we describe the close connections between Prony--like methods, namely the classical Prony method, the matrix pencil method and the ESPRIT method. Further we present a new efficient algorithm of matrix pencil factorization based on QR decomposition of a rectangular Hankel matrix. The algorithms of parameter estimation are also applied to sparse Fourier approximation and nonlinear approximation. Parameterschätzung Prony-like Methoden Fourier Approximation Parameter estimation nonincreasing exponential sum Prony-like method exponential fitting problem ESPRIT matrix pencil factorization companion matrix Prony polynomial eigenvalue problem rectangular Hankel matrix nonlinear approximation sparse trigonometric polynomial sparse Fourier approximation AMS SC: 65D10 41A45 65F15 65F20 94A12 ddc:515 Parameterschätzung Hankel-Matrix
4	Parameter estimation for nonincreasing exponential sums by Prony-like methods Potts, Daniel, Tasche, Manfred January 2012 (has links) For noiseless sampled data, we describe the close connections between Prony--like methods, namely the classical Prony method, the matrix pencil method and the ESPRIT method. Further we present a new efficient algorithm of matrix pencil factorization based on QR decomposition of a rectangular Hankel matrix. The algorithms of parameter estimation are also applied to sparse Fourier approximation and nonlinear approximation. info:eu-repo/classification/ddc/515 ddc:515 Parameterschätzung; Hankel-Matrix

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