Function Spaces on Networks

  • Delio Mugnolo
Part of the Understanding Complex Systems book series (UCS)


The first step in the study of evolution equations is the choice of suitable functions spaces that capture the structure of the problem. In this chapter we introduce some relevant spaces of functions on networks. We assume the theory of Lebesgue spaces to be known to the reader, whilst the fundamental aspects of the theory of Sobolev spaces are summarized in the Appendix B. Throughout this chapter
$$\displaystyle{\fbox{$\mathsf{G} = (\mathsf{V},\mathsf{E},\rho )\quad \text{is a weighted oriented graph}.$}}$$


Sobolev Space Lebesgue Space Lattice Ideal Geometric Graph Ultrametric Space 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Delio Mugnolo
    • 1
  1. 1.Universität Ulm Institut für AnalysisUlmGermany

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