Polynomial approximation in weighted Dirichlet spaces

2020/11/04 by Javad Mashreghi, Thomas Ransford, Mashreghi, Javad +1
Mathematics · #30H99 (secondary) #41A10 (primary) 30E10 #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #math.CV #math.FA #msc:30E10 #msc:30H99 #msc:41A10

paper · pdf · doi:10.48550/arxiv.2011.02844

arxiv created 2020/11/04 · arxiv updated 2020/11/06

Abstract

We give an elementary proof of an analogue of Fejér's theorem in weighted Dirichlet spaces with superharmonic weights. This provides a simple way of seeing that polynomials are dense in such spaces.

Related

• Bernstein's problem on weighted polynomial approximation
• Weighted approximation in ℂ
• De Branges' theorem on approximation problems of Bernstein type
• Dirichlet spaces with superharmonic weights and de Branges-Rovnyak spaces
• Approximation by polynomials in a weighted space of infinitely differentiable functions