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Global Pseudo-Differential Calculus on Euclidean Spaces

  • Fabio Nicola
  • Luigi Rodino

Part of the Pseudo-Differential Operators book series (PDO, volume 4)

Table of contents

  1. Front Matter
    Pages i-x
  2. Fabio Nicola, Luigi Rodino
    Pages 1-7
  3. Fabio Nicola, Luigi Rodino
    Pages 9-14
  4. Fabio Nicola, Luigi Rodino
    Pages 15-66
  5. Fabio Nicola, Luigi Rodino
    Pages 67-127
  6. Fabio Nicola, Luigi Rodino
    Pages 129-151
  7. Fabio Nicola, Luigi Rodino
    Pages 153-201
  8. Fabio Nicola, Luigi Rodino
    Pages 203-225
  9. Fabio Nicola, Luigi Rodino
    Pages 227-286
  10. Back Matter
    Pages 287-306

About this book

Introduction

This book is devoted to the global pseudo-differential calculus on Euclidean spaces and its applications to geometry and mathematical physics, with emphasis on operators of linear and non-linear quantum physics and travelling waves equations. The pseudo-differential calculus presented here has an elementary character, being addressed to a large audience of scientists. It includes the standard classes with global homogeneous structures, the so-called G and gamma operators. Concerning results for the applications, a first main line is represented by spectral theory. Beside complex powers of operators and asymptotics for the counting function, particular attention is here devoted to the non-commutative residue in Euclidean spaces and the Dixmier trace. Second main line is the self-contained presentation, for the first time in a text-book form, of the problem of the holomorphic extension of the solutions of the semi-linear globally elliptic equations. Entire extensions are discussed in detail. Exponential decay is simultaneously studied.

Keywords

Schrödinger operator calculus differential equation hypoelliptic operator pseudo-differential calculus

Authors and affiliations

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

Bibliographic information