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On a new kind of 2-periodic trigonometric interpolation

Tianzi Jiang, Songde Ma (1996)

Applications of Mathematics

It is well-known that the interpolation theory plays an important role in many fields of computer vision, especially in surface reconstruction. In this paper, we introduce a new kind of 2-period interpolation of functions with period 2 π . We find out the necessary and sufficient conditions for regularity of this new interpolation problem. Moreover, a closed form expression for the interpolation polynomial is given. Our interpolation is of practical significance. Our results provide the theoretical...

On a Problem of Best Uniform Approximation and a Polynomial Inequality of Visser

M. A. Qazi (2014)

Bulletin of the Polish Academy of Sciences. Mathematics

In this paper, a generalization of a result on the uniform best approximation of α cos nx + β sin nx by trigonometric polynomials of degree less than n is considered and its relationship with a well-known polynomial inequality of C. Visser is indicated.

On a Szegö's theorem of orthogonal polynomials.

Jesús Sánchez Dehesa (1979)

Revista Matemática Hispanoamericana

It is found that the asymptotical density of zeros of a system of orthogonal polynomials whose weight function belongs to a wide class of distribution functions has the expression ρ(x) = π-1 (1 - x2)-1/2. This result is shown in two completely different ways: (1) from a Szegö theorem and (2) from a Geronimus theorem and a finding recently obtained by the author in a context of Jacobi matrices.

On a Theorem of Ingham.

S. Jaffard, M. Tucsnak, E. Zuazua (1997)

The journal of Fourier analysis and applications [[Elektronische Ressource]]

On a weak type (1,1) inequality for a maximal conjugate function

Nakhlé Asmar, Stephen Montgomery-Smith (1997)

Studia Mathematica

In their celebrated paper [3], Burkholder, Gundy, and Silverstein used Brownian motion to derive a maximal function characterization of H p spaces for 0 < p < ∞. In the present paper, we show that the methods in [3] extend to higher dimensions and yield a dimension-free weak type (1,1) estimate for a conjugate function on the N-dimensional torus.

On | A , δ | k -summability of orthogonal series

Xhevat Z. Krasniqi (2012)

Mathematica Bohemica

In the paper, we prove two theorems on | A , δ | k summability, 1 ≤ k ≤ 2 , of orthogonal series. Several known and new results are also deduced as corollaries of the main results.

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