Potential operators associated with Jacobi and Fourier–Bessel expansions

Periodic Jacobi-Perron expansions associated with a unit

We prove that, for any unit in a real number fieldK of degree n+ 1, there exits only a finite number of n-tuples in K which have a purely periodic expansion by the Jacobi-Perron algorithm. This generalizes the case of continued fractions for n = 1. For n = 2 we give an explicit algorithm to compute all these pairs.

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

Calderón-zygmund Operators Associated to Ultraspherical Expansions

Submajorization inequalities associated with $tau$-measurable operators

The aim of this note is to study the submajorization inequalities for $tau$-measurable operators in a semi-finite von Neumann algebra on a Hilbert space with a normal faithful semi-finite trace $tau$. The submajorization inequalities generalize some results due to Zhang, Furuichi and Lin, etc..