«chebyshev systems»
۱۱۲۱ نتیجهChebyshev systems and zeros of a function on a convex curve
The classical Hurwitz theorem says that if n first “harmonics” (2n+1 Fourier coefficients) of a continuous function f(x) on the unit circle are zero, then f(x) changes sign at least 2n + 1 times. We show that similar facts and its converse hold for any function that are orthogona
Self-Concordant Barriers for Cones Generated by Chebyshev Systems
We explicitly calculate characteristic functions of cones of generalized polynomials corresponding to Chebyshev systems on intervals of the real line and the circle. Thus, in principle, we calculate homogeneous self-concordant barriers for this class of cones. This class includes
An extended complete Chebyshev system of 3 Abelian integrals related to a non-algebraic Hamiltonian system
In this paper, we study the Chebyshev property of the 3-dimentional vector space $E =\langle I_0, I_1, I_2\rangle$, where $I_k(h)=\int_{H=h}x^ky\,dx$ and $H(x,y)=\frac{1}{2}y^2+\frac{1}{2}(e^{-2x}+1)-e^{-x}$ is a non-algebraic Hamiltonian function. Our main result asserts that $E
Multidimensional Chebyshev Systems - just a definition
We provide a definition of Multidimensional Chebyshev Systems of order N which is satisfied by the solutions of a wide class of elliptic equations of order 2N . This definition generalizes a very large class of Extended Complete Chebyshev systems in the one-dimensional case. This
On the Chebyshev Property for a New Family of Functions
We analyze whether a given set of analytic functions is an Extended Chebyshev system. This family of functions appears studying the number of limit cycles bifurcating from some nonlinear vector field in the plane. Our approach is mainly based on the so called Derivation-Division
Variable degree polynomial splines are Chebyshev splines
Variable degree polynomial (VDP) splines have recently proved themselves as a valuable tool in obtaining shape preserving approximations. However, some usual properties which one would expect of a spline space in order to be useful in geometric modeling, do not follow easily from
Small Chebyshev systems made by products
A new characterization of convexity with respect to Chebyshev systems
Characterizations of higher-order convexity properties with respect to Chebyshev systems
Best L1 approximation by weak chebyshev systems and the uniqueness of interpolating perfect splines