The Problem of the Completeness of Systems of Particular Solutions of Partial Differential Equations

  • Gaetano Fichera
Part of the ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique book series (ISNM, volume 49)

Abstract

Let K be a compact set of the plane of the complex variable z = x + iy and Ω(K) the vector space of complex valued functions f(z) defined on K, continuous on K and holomorphic in any interior point of K (if any). If Ω(K)is endowed with the norm
$$ \left\| {f(z)\left\| {\mathop {\max }\limits_K \left| {f(z)\left| , \right.} \right.} \right.} \right. $$
it becomes a Banach space.

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© Springer Basel AG 1979

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  • Gaetano Fichera

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