On the Result of Invariance of the Closure Set of the Real Projections of the Zeros of an Important Class of Exponential Polynomials

In this paper we provide the proof of a practical point-wise characterization of the set RP defined by the closure set of the real projections of the zeros of an exponential polynomial P(z) = Σn j=1 cjewjz with real frequencies wj linearly independent over the rationals. As a consequence, we give a complete description of the set RP and prove its invariance with respect to the moduli of the c′ js, which allows us to determine exactly the gaps of RP and the extremes of the critical interval of P(z) by solving inequations with positive real numbers. Finally, we analyse the converse of this result of invariance.

Thom Darden pressures QB Phipps, UM Football vs Purdue, 1969

[Thom Darden (35,), Fred Grambau (92)]

Line and area orthogonality of Jacobi polynomials,

"Supported in part by contract U.S. AEC AT(11-1) 1469 and grant NSF-6J-217".

Orthogonality relations for Chebyshev polynomials,

"C00-1469-0154."

Parallel methods and bounds of evaluating polynomials.

Bibliography: p. 24.

The use of Chebyshev matrix polynomials in the iterative solution of linear equations compared to the method of successive overrelaxtion /

"(This is being submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics, June 1959.)"

Guilielmi Neubrigensis Historia sive Chronica rerum anglicarum, libris quinque. E codice ms. pervetusto, in bibliotheca prænobilis domini Dni. Thomæ Sebright.

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