Convergence to Zero of Exponential Sums with Positive Integer Coefficients and Approximation by Sums of Shifts of a Single Function on the Line
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DOI: 10.1007/s10476-018-0204-2
Abstract: We prove that there is a sequence of trigonometric polynomials with positive integer coefficients, which converges to zero almost everywhere. We also prove that there is a function f: ℝ → ℝ such that the… read more here.
Keywords: convergence zero; sums shifts; integer coefficients; positive integer ... See more keywords
On the Stability of Linear Dynamic Controllers With Integer Coefficients
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DOI: 10.1109/tac.2021.3131126
Abstract: In this article, we show that linear dynamic controllers with integer coefficients are usually unstable. In fact, asymptotic stability can only be achieved if all controller eigenvalues are equal to zero. Moreover, for a fixed… read more here.
Keywords: controllers integer; linear dynamic; dynamic controllers; integer coefficients ... See more keywords
Chebyshev Polynomials and Integer Coefficients
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DOI: 10.1134/s0001434619010322
Abstract: Generalized Chebyshev polynomials are introduced and studied in this paper. They are applied to obtain a lower bound for the sup-norm on the closed interval for nonzero polynomials with integer coefficients of arbitrary degree. read more here.
Keywords: chebyshev polynomials; polynomials integer; integer coefficients;