Failure of Approximation of Odd Functions by Odd Polynomials

30 Jun 2020 Mashreghi Javad Parisé Pierre-Olivier Ransford Thomas

We construct a Hilbert holomorphic function space $H$ on the unit disk such that the polynomials are dense in $H$, but the odd polynomials are not dense in the odd functions in $H$. As a consequence, there exists a function $f$ in $H$ that lies outside the closed linear span of its Taylor partial sums $s_n(f)$, so it cannot be approximated by any triangular summability method applied to the $s_n(f)$... (read more)

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Categories


  • FUNCTIONAL ANALYSIS
  • CLASSICAL ANALYSIS AND ODES
  • COMPLEX VARIABLES