The Gauss–Borel or LU factorization of Gram matrices bilinear forms is the pivotal element in discussion theory biorthogonal polynomials. construction families polynomials and its second kind functions, spectral modeling multiplication by independent variable x, Christoffel–Darboux kernel projection properties, are discussed from this point view. Then, Hankel case presented different specific c...

We obtain upper bounds for Lebesgue constants (uniform norms) of hyperinterpolation operators via estimates for (the reciprocal of) Christoffel functions, with different measures on the disk and ball, and on the square and cube. As an application, we show that the Lebesgue constant of total-degree polynomial interpolation at the Morrow-Patterson minimal cubature points in the square has an O(de...

To perform a non-destructive evaluation of wood, the Christoffel equation is frequently used to describe the relationship between the ultrasonic wave velocity and the mechanical parameters. In the context of acoustical tomography imaging of standing trees, the key contribution of this numerical study is to determine the influence of mechanical parameters of the wood radial-tangential plane on t...

Optimal light absorption is decisive in obtaining high-efficiency solar cells. An established, if not to say the approach texture interface of light-absorbing layer with a suitable microstructure. However, structuring detrimental concerning its electrical properties due an increased surface recombination rate (owing enlarged area and defects) caused by direct patterning process itself. This eff...