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

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Numerical Mathematics / Numerische Mathematik

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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Authors
  1. Gaetano Fichera
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R. Ansorge K. Glashoff B. Werner

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© 1979 Springer Basel AG

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Fichera, G. (1979). The Problem of the Completeness of Systems of Particular Solutions of Partial Differential Equations. In: Ansorge, R., Glashoff, K., Werner, B. (eds) Numerical Mathematics / Numerische Mathematik. ISNM International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale D’Analyse Numérique, vol 49. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6285-1_2

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  • DOI: https://doi.org/10.1007/978-3-0348-6285-1_2

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-6286-8

  • Online ISBN: 978-3-0348-6285-1

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