Fast algorithms for discrete Chebyshev-Vandermonde transforms and applications

Applying orthogonal polynomials, the discrete Chebyshev-Vandermonde transform (DCVT) is introduced as a special almost orthogonal transform. An important example of DCVT is the discrete cosine transform (DCT). Using the divide-and-conquer technique and the d'Alembert functional equation, fast DCT-algorithms are described. By the help of these results we present for the first time fast, numerically stable algorithms for simultaneous polynomial approximation and for collocation method for the airfoil equation, a special Cauchytype singular integral equation.     

Continuity and Fréchet-differentiability of Nemytskij operators in Hölder spaces

The paper is devoted to superposition operators acting between Hölder spaces, for which we prove continuity properties and Fréchet-differentiability under assumptions being weaker than those so far known in the literature.     

Unique solvability of the periodic Cauchy problem for wave-hierarchy problems with dissipation

Wave-hierarchy problems appear in a variety of applications such as traffic flows, roll waves down an open inclined channel and multiphase flows. Usually, these are described by the compressible Navier-Stokes equations with specific non-linearities; in a fluidized bed model they contain an additional pressure gradient term and are supplemented by an elliptic equation for this unknown pressure. These equations admit solutions periodic in space as well as in time, i.e. periodic travelling waves. Therefore, the corresponding initial value problem with periodic boundary conditions is solved locally in time in appropriate Sobolev spaces. Some remarks are made concerning global solutions, the occurrence of clusters or voids and the bifurcation of time periodic solutions, respectively.     

Industrial applications of excimer lasers

Possible industrial applications of excimer lasers are discussed.     

A class of Nevanlinna functions related to singular Sturm-Liouville problems

The class of Nevanlinna functions consists of functions which are holomorphic off the real axis, which are symmetric with respect to the real axis, and whose imaginary part is nonnegative in the upper halfplane. The Kac subclass of Nevanlinna functions is defined by an integrability condition on the imaginary part. In this note a further subclass of these Kac functions is introduced. It involves an integrability condition on the modulus of the Nevanlinna functions (instead of the imaginary part). The characteristic properties of this class are investigated. The definition of the new class is motivated by the fact that the Titchmarsh-Weyl coefficients of various classes of Sturm-Liouville problems (under mild conditions on the coefficients) actually belong to this class.