Approximations in L¹ with convergent Fourier series

2018/10/14 by Avetisyan, Zhirayr, Grigoryan, Martin, Ruzhansky, Michael
#41A99 #43A15 #43A50 #43A85 #46E30 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1810.06047

Abstract

For a separable finite diffuse measure space M and an orthonormal basis \φ_n\ of L²(M) consisting of bounded functions φ_n∈ L^∞(M), we find a measurable subset E\subsetM of arbitrarily small complement |M∖ E|

Related

• A constrained approximation theorem for integral functionals on L^p
• A uniformly bounded complete Euclidean system
• Construction of function spaces close to L^∞ with associate space close to L¹
• Revisiting mean-square approximation by polynomials in the unit disk
• On a distinctive property of Fourier bases associated with N- Bernoulli Convolutions