6533b7ddfe1ef96bd1273e1c
RESEARCH PRODUCT
On the Almost Everywhere Convergence of Multiple Fourier-Haar Series
Francesco TuloneGiorgi Onianisubject
40A05Control and OptimizationBounded set (topological vector space)Type (model theory)01 natural sciencesmultiple Fourier-Haar seriesHomothetic transformationCombinatoricssymbols.namesakeSettore MAT/05 - Analisi Matematica0103 physical sciences42C10Almost everywhere0101 mathematicsMathematicsSeries (mathematics)Applied Mathematics010102 general mathematicsRegular polygonAlmost everywhere convergenceFunction (mathematics)Fourier transformsymbols010307 mathematical physicslacunar serieAnalysisdescription
The paper deals with the question of convergence of multiple Fourier-Haar series with partial sums taken over homothetic copies of a given convex bounded set $$W\subset\mathbb{R}_+^n$$ containing the intersection of some neighborhood of the origin with $$\mathbb{R}_+^n$$ . It is proved that for this type sets W with symmetric structure it is guaranteed almost everywhere convergence of Fourier-Haar series of any function from the class L(ln+L)n−1.
year | journal | country | edition | language |
---|---|---|---|---|
2019-09-01 | Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences) |