2012, English, French, Book edition: Phase-space analysis and pseudodifferential calculus on the Heisenberg group / Hajer Bahouri & Clotilde Fermanian-Kammerer & Isabelle Gallagher. Bahouri, Hajer.

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Phase-space analysis and pseudodifferential calculus on the Heisenberg group / Hajer Bahouri & Clotilde Fermanian-Kammerer & Isabelle Gallagher
 
Bookmark: https://trove.nla.gov.au/version/181726208
Physical Description
  • 127 p. ; 24 cm.
Published
  • Paris Societé mathématique de France, [2012]
Language
  • English
  • French

Edition details

Title
  • Phase-space analysis and pseudodifferential calculus on the Heisenberg group /​ Hajer Bahouri &​ Clotilde Fermanian-Kammerer &​ Isabelle Gallagher.
Also Titled
  • Pseudodifferential calculus on the Heisenberg group
Author
  • Bahouri, Hajer.
Other Authors
  • Fermanian-Kammerer, Clotilde.
  • Gallagher, Isabelle.
Published
  • Paris Societé mathématique de France, [2012]
Copyright
  • ©2012
Content Types
  • text
Carrier Types
  • volume
Physical Description
  • 127 p. ; 24 cm.
Series
Part Of
  • Astérisque no:342 0303-1179
Subjects
Contents
  • Machine generated contents note: 1.Introduction and main results
  • 1.1.Introduction
  • 1.1.1.The Heisenberg group
  • 1.1.2.Microlocal analysis on Rn
  • 1.1.3.Microlocal analysis on the Heisenberg group
  • 1.1.4.Structure of the paper
  • Acknowledgements
  • 1.2.Basic facts on the Heisenberg group Hd
  • 1.2.1.The Heisenberg group
  • 1.2.2.Irreducible representations and the Fourier transform
  • 1.3.Weyl-Hormander calculus
  • 1.3.1.Admissible weights and metrics
  • 1.3.2.The case of the harmonic oscillator
  • 1.4.Main results: pseudodifferential operators on the Heisenberg group
  • 1.4.1.Symbols
  • 1.4.2.Operators
  • 1.4.3.Statement of the results
  • 2.Fundamental properties of pseudodifferential operators
  • 2.1.Examples of pseudodifferential operators
  • 2.1.1.Multiplication operators
  • 2.1.2.Generalized multiplication operators
  • 2.1.3.Differentiation operators
  • 2.1.4.Fourier multipliers
  • 2.2.The link between the kernel and the symbol of a pseudodifferential operator
  • Contents note continued: 2.3.Action on the Schwartz class
  • 3.The algebra of pseudodifferential operators
  • 3.1.The adjoint of a pseudodifferential operator
  • 3.2.Proof of Proposition 3.1
  • 3.3.Study of the composition of two pseudodifferential operators
  • 3.4.The asymptotic formulas
  • 4.Littlewood-Paley theory
  • 4.1.Littlewood-Paley operators
  • 4.2.Besov spaces
  • 4.3.Truncation pseudodifferential operators
  • 4.4.λ-truncation operators
  • 4.5.The symbol of Littlewood-Paley operators
  • 5.The action of pseudodifferential operators on Sobolev spaces
  • 5.1.Reduction to the case of operators of order zero
  • 5.2.Reduction to the case of a fixed regularity index
  • 5.3.Reduced and reduceable symbols
  • 5.4.Decomposition into reduced symbols and proof of the theorem
  • 5.5.Proof of Proposition 5.2
  • 5.5.1.Reductions
  • 5.5.2.Spectral localization
  • 5.5.3.The remainder term
  • 5.5.4.The high frequencies
  • 5.5.5.The low frequencies
  • Contents note continued: A.Some useful results on the Heisenberg group
  • A.1.Left invariant vector fields
  • A.2.Bargmann and Schrodinger representations
  • A.2.1.Connexion between the representations
  • A.2.2.Some useful formulas
  • B.Weyl-Hormander symbolic calculus on the Heisenberg group
  • B.1.λ-dependent metrics
  • B.2.λ-dependent symbols
  • B.3.Symbols of functions of the harmonic oscillator
  • B.4.The symbol of Littlewood-Paley operators on the Heisenberg group.
Notes
  • Includes bibliographical references (p. [123]-127)
  • Abstract also in French.
Language
  • English
  • French
ISBN
  • 9782856293348 (pbk.)
  • 2856293344 (pbk.)
Dewey Number
  • 510.5
Libraries Australia ID
Contributed by
Libraries Australia

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