The q-classical polynomials are orthogonal polynomial sequences that are eigenfunctions of a second order q-differential operator of a certain type. We explicitly construct q-differential equations of arbitrary even order fulfilled by these polynomials, while giving explicit expressions for the integer composite powers of the aforementioned second order q-differential operator. The latter is ac...

In this paper, we present an analysis of a multigrid method for nonsym-metric and/or indeenite elliptic problems. In this multigrid method various types of smoothers may be used. One type of smoother which we consider is deened in terms of an associated symmetric problem and includes point and line, Jacobi and Gauss-Seidel iterations. We also study smoothers based entirely on the original opera...

It is proved that given a divergence operator on the structural sheaf of graded commutative algebras of a supermanifold, it is possible to construct a generating operator for the Krashil’shchik-Schouten bracket. This is a particular case of the construction of generating operators for a special class of bigraded Gerstenhaber algebras. Also, some comments on the generalization of these results t...

In this paper, we study the Gauss map of a free boundary minimal surface. The main theorem asserts that if components are eigenfunctions Jacobi-Steklov operator, then surface must be rotationally symmetric.

The Jacobi polynomials induce a translation operator on function spaces on the interval [−1, 1]. For any homogeneous Banach space B w.r.t. this translation, we can study the according little and big Lipschitz spaces, lipB(λ) and LipB(λ), respectively. The big Lipschitz spaces are not homogeneous themselves. Therefore we introduce semihomogeneous Banach spaces w.r.t. Jacobi translation, of which...