The theorem proved here extends Chebyshev theory into what has previously been no man's land: functions which have an infinite number of bounded derivatives on the expansion interval [a, b] but which are singular at one endpoint. The Chebyshev series in l/x for all the familiar special functions fall into this category, so this class of functions is very important indeed. In words, the theorem ...

We obtain a property which characterizes the Chebyshev orthogonal polynomials of first, second, third, and fourth kind. Indeed, we prove that the four Chebyshev sequences are the unique classical orthogonal polynomial families such that their linear combinations, with fixed length and constant coefficients, can be orthogonal polynomial sequences. 1. Introduction The classical orthogonal polynom...

Abstract We develop a diagrammatic categorification of the polynomial ring Z[x], based on geometrically defined graded algebra. This construction generalizes to some special functions, such as Chebyshev polynomials. Diagrammatic algebras featured in these categorifications lead first topological interpretations Bernstein-Gelfand-Gelfand reciprocity property.

The classical Chebyshev theory of best uniform approximation to continuous functions by polynomials of degree <n was initiated by Chebyshev in [2]. This theory has a distinct advantage over the corresponding ones for L4-norms, 1 < q < co, in that the unique best approximant is characterized by a remarkable geometric property. Let f be a realvalued function, continuous on [0, 11, and, for n = 0,...

An explicit method to compute algebraic equations of curves constant width and Zindler generated by a family middle hedgehogs is given thanks property Chebyshev polynomials. This extends the methodology used Rabinowitz Martinez-Maure in particular generate full equations, both curves, defined trigonometric polynomials as support functions.

In the present paper we give a characterization of Chebyshev subspaces in the space of (real or complex) continuously-differentiable functions of two variables. We also discuss various applications of the characterization theorem. Introduction. One of the central problems in approximation theory consists in determining the best approximation; that is, in a normed linear space X with a prescribe...

This paper proposes an improved public key encryption algorithm based on Chebyshev polynomials. On the base of the semi-group property of Chebyshev polynomials, we import the alternative multiply coefficient i K to forge the ciphertext tactfully which can make the cipher text-only aattack out of work. The chosen of i K is decided by the value of ( ( )) mod r s T T x N , and the number of i K ca...

Working over a field k of characteristic zero, this paper studies line embeddings of the form φ = (Ti, Tj , Tk) : A → A, where Tn denotes the degree n Chebyshev polynomial of the first kind. In Section 4, it is shown that (1) φ is an embedding if and only if the pairwise greatest common divisor of i, j, k is 1, and (2) for a fixed pair i, j of relatively prime positive integers, the embeddings ...