Exponential Decay and Holomorphic Extension of Solutions

  • Fabio Nicola
  • Luigi Rodino
Part of the Pseudo-Differential Operators book series (PDO, volume 4)


In the preceding chapters we proved, under different assumptions of global hypoellipticity on the symbol in ℝ d , that the solutions in \( S'\left( {\mathbb{R}^d } \right) \) of the homogeneous equation belong to \( S\left( {\mathbb{R}^d } \right) \). In particular, for the self-adjoint operators discussed in Chapter 4, all the eigenfunctions belong to \( S\left( {\mathbb{R}^d } \right) \). In the present chapter we show that this information can be strongly improved for G and Γ operators, namely we may give precise results of exponential decay and holomorphic extension of solutions.


Banach Space Solitary Wave Exponential Decay Entire Function Complex Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Basel AG 2010

Authors and Affiliations

  • Fabio Nicola
    • 1
  • Luigi Rodino
    • 2
  1. 1.Dipartimento di MatematicaPolitecnico di TorinoTorinoItaly
  2. 2.Dipartimento di MatematicaUniversità di TorinoTorinoItaly

Personalised recommendations