From (β,γ)-Chebyshev functions of the interval to (β,γ)-Lissajous curves of the square
Stefano De Marchi  1  , Giacomo Elefante  1  , Francesco Marchetti  1@  
1 : Dipartimento di Matematica ``Tullio Levi-Civita'' -- Università degli Studi di Padova

The (β,γ)-Chebyshev functions and points, which we studied recently, generalise the classical Chebyshev polynomials and related points, and can be employed effectively in polynomial interpolation tasks on the interval [-1,1]. On the other hand, unions of tensor-product Chebyshev grids provide sets of nodes that guarantee a stable polynomial interpolation process on the square [-1,1]^2, and that can be characterised as self-intersection or square-tangency points of Lissajous curves. Therefore, this paves the way for the study of (β,γ)-Chebyshev grids and for the analysis of polynomial approximation schemes along (β,γ)-Lissajous curves in [-1,1]^2, in view of designing a unified generalised framework. Joint work with Stefano De Marchi and Giacomo Elefante.

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