A+ CATEGORY SCIENTIFIC UNIT

The space of real-analytic functions has no basis

Volume 142 / 2000

Paweł Domański, Dietmar Vogt Studia Mathematica 142 (2000), 187-200 DOI: 10.4064/sm-142-2-187-200

Abstract

Let Ω be an open connected subset of $ℝ^d$. We show that the space A(Ω) of real-analytic functions on Ω has no (Schauder) basis. One of the crucial steps is to show that all metrizable complemented subspaces of A(Ω) are finite-dimensional.

Authors

  • Paweł Domański
  • Dietmar Vogt

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