Generalized Jacobi–Weierstrass operators and Jacobi expansions

Generalized Jacobi Operators in Krein Spaces

A special class of generalized Jacobi operators which are self-adjoint in Krein spaces is presented. A description of the resolvent set of such operators in terms of solutions of the corresponding recurrence relations is given. In particular, special attention is paid to the periodic generalized Jacobi operators. Finally, the spectral properties of generalized Jacobi operators are applied to pr...

Maximal Operators Associated with Generalized Hermite Polynomial and Function Expansions

We study the weak and strong type boundedness of maximal heat–diffusion operators associated with the system of generalized Hermite polynomials and with two different systems of generalized Hermite functions. We also give a necessary background to define Sobolev spaces in this context.

Product Jacobi Expansions 3

Generalized De La Vallée Poussin Operators for Jacobi Weights

Starting from a natural generalization of the trigonometric case, we construct a de la Vallée Poussin approximation process in the uniform and L norms. With respect to the classical approach we obtain the convergence for a wider class of Jacobi weights. Even if we only consider the Jacobi case, our construction is very general and can be extended to other classes of weights.

On Generalized Carleson Operators of Periodic Wavelet Packet Expansions

Three new theorems based on the generalized Carleson operators for the periodic Walsh-type wavelet packets have been established. An application of these theorems as convergence a.e. for the periodic Walsh-type wavelet packet expansion of block function with the help of summation by arithmetic means has been studied.