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Global Pseudo-Differential Calculus

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

Abstract

Pseudo-differential operators, in a broad sense, are linear operators of the type
$$ a\left( {x,D} \right)u\left( x \right) = \int {e^{ix\xi } a\left( {x,\xi } \right)\hat u\left( \xi \right)d--\xi ,} u \in S\left( {\mathbb{R}^d } \right). $$
(1.0.1)
The function a(x, ξ), satisfying suitable estimates in ℝ2d, is called the symbol of a(x, D). In fact, (1.0.1) makes sense as a temperate distribution even for \( a \in S'\left( {\mathbb{R}^d } \right) \).

Keywords

Asymptotic Expansion Sobolev Space Fredholm Operator Fredholm Property Schwartz Function 
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.

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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

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