Concerning Extended Complete Tchebycheff system

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 $E =langle I_0, I_1, I_2rangle$, 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 $E$ is an extended complete Chebyshev space for $hin(0,frac{1}{2})$. To this end, we use the criterion and tools developed by...

Investigations Concerning the Structure of Complete Sets

This paper will discuss developments bearing on three related research directions where Somenath Biswas has made pioneering contributions: • Isomorphism of Complete Sets • Creative Sets • Universal Relations Some open questions in each of these directions will be highlighted. Mathematics Subject Classification (2010). Primary 68Q15.

Combinatorics of generalized Tchebycheff polynomials

By considering a family of orthogonal polynomials generalizing the Tchebycheff polynomials of the second kind we refine the corresponding results of De Sainte-Catherine and Viennot on Tchebycheff polynomials of the second kind (Lecture Notes in Mathematics, vol. 1171, 1985, Springer-Verlag, 120). © 2003 Elsevier Science Ltd. All rights reserved.

Tchebycheff Approximation in a Compact Metric Space

On a class of weak Tchebycheff systems

In this paper we study the approximation power, the existence of a normalized B-basis and the structure of a degree-raising process for spaces of the form span < 1, x, . . . , x, u(x), v(x) >, requiring suitable assumptions on the functions u and v. The results about degree raising are detailed for special spaces of this form which have been recently introduced in the area of CAGD.