Une classe de symboles new-look

André Hirschowitz

Annales de l'institut Fourier (1980)

  • Volume: 30, Issue: 3, page 199-217
  • ISSN: 0373-0956

Abstract

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We construct, in a geometric way, a class of symbols which are classical except along some submanifold. The parametrics of ∑ i = 1 n - 1 ∂ ∂ x i 4 + ∂ ∂ x n 3 and ∂ ∂ x n 3 + ∑ i = 1 n - 1 ∂ ∂ x i 2 , for instance, belong to the associated class of pseudodifferential operators.

How to cite

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Hirschowitz, André. "Une classe de symboles new-look." Annales de l'institut Fourier 30.3 (1980): 199-217. <http://eudml.org/doc/74459>.

@article{Hirschowitz1980,
abstract = {On construit par voie géométrique une classe de symboles classiques en dehors d’une sous-variété. La classe d’opérateurs pseudodifférentiels associée contient les paramétrix d’opérateurs tels que $\sum ^\{n-1\}_\{i=1\}\big (\{\partial \over \partial x_i\}\big )^4 +\big (\{\partial \over \partial x_n\}\big )^3$ ou $\big (\{\partial \over \partial x_n\}\big )^3+ \sum ^\{n-1\}_\{i=1\} \big (\{\partial \over \partial x_i\}\big )^2.$},
author = {Hirschowitz, André},
journal = {Annales de l'institut Fourier},
keywords = {pseudodifferential operators; hypoelliptic operators; parametrices},
language = {fre},
number = {3},
pages = {199-217},
publisher = {Association des Annales de l'Institut Fourier},
title = {Une classe de symboles new-look},
url = {http://eudml.org/doc/74459},
volume = {30},
year = {1980},
}

TY - JOUR
AU - Hirschowitz, André
TI - Une classe de symboles new-look
JO - Annales de l'institut Fourier
PY - 1980
PB - Association des Annales de l'Institut Fourier
VL - 30
IS - 3
SP - 199
EP - 217
AB - On construit par voie géométrique une classe de symboles classiques en dehors d’une sous-variété. La classe d’opérateurs pseudodifférentiels associée contient les paramétrix d’opérateurs tels que $\sum ^{n-1}_{i=1}\big ({\partial \over \partial x_i}\big )^4 +\big ({\partial \over \partial x_n}\big )^3$ ou $\big ({\partial \over \partial x_n}\big )^3+ \sum ^{n-1}_{i=1} \big ({\partial \over \partial x_i}\big )^2.$
LA - fre
KW - pseudodifferential operators; hypoelliptic operators; parametrices
UR - http://eudml.org/doc/74459
ER -

References

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  1. [1] L. BOUTET DE MONVEL, Hypoelliptic operators with double characteristics and related pseudodifferential operators, Comm. Pure and Appl. Math., XXVII (1974), 585-639. Zbl0294.35020MR51 #6498
  2. [2] J.J. DUISTERMAAT, Fourier Integral Operators, Courant Institute of Math. Sciences, New York University, 1973. Zbl0272.47028MR56 #9600
  3. [3] J.J. DUISTERMAAT, Oscillatory Integrals, Lagrange Immersions and Unfolding of Singularities, Comm. Pure and Appl. Math., XXVII (1974), 207-281. Zbl0285.35010MR53 #9306
  4. [4] J.J. DUISTERMAAT, L. HÖRMANDER, Fourier Integral Operators II, Acta Math., 128 (1972), 183-265. Zbl0232.47055MR52 #9300
  5. [5] V. GUILLEMIN, Singular Symbols, Preprint, 1975. 
  6. [6] B. HELFFER, Invariants associés à une classe d'opd et applications à l'hypoellipticité, Ann. Inst. Fourier, XXVI Fasc. 2 (1976), 55-70. Zbl0301.35026MR54 #1318
  7. [7] L. HÖRMANDER, Hypoelliptic differential operators, Ann. Inst. Fourier, XI (1961), 477-492. Zbl0099.30101MR23 #A3368
  8. [8] L. HÖRMANDER, Fourier Integral Operators I, Acta Math., 127 (1971), 79-183. Zbl0212.46601MR52 #9299

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