Polynomial approximation in weighted Dirichlet spaces

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.

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Bibliographic Details
Published in:Complex analysis and its synergies 2021-06, Vol.7 (2), Article 11
Main Authors: Mashreghi, Javad, Ransford, Thomas
Format: Article
Language:English
Subjects:
Algebraic Geometry
Analysis
Complex Analysis: a Renewable Resource for Techniques and Problems in Mathematics
Dirichlet problem
Dynamical Systems and Ergodic Theory
Functional Analysis
Functions of a Complex Variable
Mathematics
Mathematics and Statistics
Partial Differential Equations
Polynomials
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Description
Summary: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.
ISSN:2524-7581
2197-120X
DOI:10.1007/s40627-021-00078-9