Suchergebnisse

The common trigonometric functions admit generalizations to any higher dimension, the symmetric, antisymmetric and alternating ones. In this paper, we restrict ourselves to three dimensional generalization only, focusing on alternating case in detail. Many specific properties of this new class of special functions useful in applications are studied. Such are the orthogonalities, both the continuous one and the discrete one on the 3D lattice of any density, corresponding discrete and continuous Fourier transforms, and others. Rapidly increasing precision of the interpolation with increasing density of the 3<em>D</em> lattice is shown in an example.

Suitable automorphisms together with complete classification of representations of some algebras can be used to generate some sets of orthogonal polynomials "at no cost". This is also the case of nonstandard Klimyk-Gavrilik deformation Uq'(so3) which is connected to q-Racah polynomials.

We discuss the construction of the Verma basis of the enveloping algebra and of finite dimensional representations of the Lie algebra An. We give an alternate proof of so-called Verma inequalities to the one given in [1] by P. Littelmann.