The Riemann-Cantor uniqueness theorem for unilateral trigonometric series via a special version of the Lusin-Privalov theorem
Journal Title: Annales Universitatis Mariae Curie-Skłodowska. Sectio A, Mathematica - Year 2017, Vol 71, Issue 1
Abstract
Using Baire's theorem, we give a very simple proof of a special version of the Lusin-Privalov theorem and deduce via Abel's theorem the Riemann-Cantor theorem on the uniqueness of the coefficients of pointwise convergent unilateral trigonometric series.
Authors and Affiliations
Raymond Mortini
On almost complex structures from classical linear connections
Let Mfm be the category of m-dimensional manifolds and local diffeomorphisms and let T be the tangent functor on Mfm. Let V be the category of real vector spaces and linear maps and let Vm be the category of m-dimension...
On generalized Mersenne numbers, their interpretations and matrix generators
In this paper we introduce generalized Mersenne numbers. We shall present some of their interpretations and matrix generators which are very useful for determining identities.
Properties of modulus of monotonicity and Opial property in direct sums
We give an example of a Banach lattice with a non-convex modulus of monotonicity, which disproves a claim made in the literature. Results on preservation of the non-strict Opial property and Opial property under passing...
Products of Toeplitz and Hankel operators on the Bergman space in the polydisk
In this paper we obtain a condition for analytic square integrable functions f, g which guarantees the boundedness of products of the Toeplitz operators TfTg densely defined on the Bergman space in the polydisk. An analo...
On almost polynomial structures from classical linear connections
Let Mfm be the category of m-dimensional manifolds and local diffeomorphisms and let T be the tangent functor on Mfm. Let V be the category of real vector spaces and linear maps and let Vm be the category of m-dimensiona...