On polynomials of least deviation from zero in several variables [PDF]
Experimental Mathematics, 2004 14 pages, 1 ...
Yuan Xu
core +10 more sources
Polynomials of Least Deviation from Zero in Sobolev p-Norm [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2022 AbstractThe first part of this paper complements previous results on characterization of polynomials of least deviation from zero in Sobolev p-norm ($$1<p<\infty $$ 1 < p < ∞ ) for the ...
Abel Díaz-González +2 more
exaly +7 more sources
Least deviation of logarithmic derivatives of algebraic polynomials from zero
Journal of Approximation Theory, 2014 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Petr Chunaev
exaly +5 more sources
Trigonometric polynomials of least deviation from zero in measure and related problems
Journal of Approximation Theory, 2010 Let \(\mathcal{F}_{n}\) be the set of trigonometric polynomials \[ f_{n}(t)=\frac{a_{0}}{2}+\sum_{k=1}^{n}(a_{k}\cos kt +b_{k}\sin k t) \] of order \(n\geq 0\) with real coefficients. On the set \(\mathcal{F}_{n}\) consider the functional \[ \mu(f_{n})=\text{mes}\{t\in \mathbb{T}\,:\,|f_{n}(t)|\geq 1\}, \] where \(\text{mes}\) stands for the Lebesgue ...
В. В. Арестов +1 more
exaly +5 more sources
On multivariate polynomials of least deviation from zero on the unit ball
Mathematische Zeitschrift, 1977 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Manfred Reimer
exaly +6 more sources
On multivariate polynomials of least deviation from zero on the unit cube
Journal of Approximation Theory, 1978 AbstractIn the family of all r-variable real polynomials with total degree not exceeding μ and with maximum norm on the unit-cube not exceeding 1, any of the leading coefficients is maximum for a special product of one-variable Chebyshev polynomials of the first kind.
Manfred Reimer
exaly +5 more sources
Bivariate Polynomials of Least Deviation from Zero [PDF]
Canadian Journal of Mathematics, 2001 AbstractBivariate polynomials with a fixed leading term xmyn, which deviate least fromzero in the uniform or L2-norm on the unit disk D (resp. a triangle) are given explicitly. A similar problem in Lp, 1 ≤ p ≤ ∞, is studied on D in the set of products of linear polynomials.
Borislav Bojanov +2 more
openalex +3 more sources
Logarithmic Derivatives of Least Deviation from Zero [PDF]
, 2014 We study least deviation of logarithmic derivatives of real-valued polynomials with a fixed root from zero on the segment $[-1;1]$ in the uniform norm with the weight $\sqrt{1-x^2}$ and without it. Basing on results of Komarov and Novak and on a certain determinant identity due to Borchardt, we also establish a criterion for best uniform approximation ...
Petr Chunaev
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POLYNOMIALS LEAST DEVIATING FROM ZERO IN \(L^p(-1;1)\), \(0 \le p \le \infty \), WITH A CONSTRAINT ON THE LOCATION OF THEIR ROOTS [PDF]
Ural Mathematical Journal, 2023 We study Chebyshev's problem on polynomials that deviate least from zero with respect to \(L^p\)-means on the interval \([-1;1]\) with a constraint on the location of roots of polynomials.
Alena E. Rokina
doaj +3 more sources
Statistical optimization for passive scalar transport: maximum entropy production versus maximum Kolmogorov–Sinai entropy [PDF]
Nonlinear Processes in Geophysics, 2015 We derive rigorous results on the link between the principle of maximum entropy production and the principle of maximum Kolmogorov–Sinai entropy for a Markov model of the passive scalar diffusion called the Zero Range Process.
M. Mihelich +3 more
doaj +8 more sources