Some remarks on almost-positivity of ψ ⁢ do 's

Cesare Parenti; Alberto Parmeggiani

Bollettino dell'Unione Matematica Italiana (1998)

  • Volume: 1-B, Issue: 1, page 187-215
  • ISSN: 0392-4041

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Parenti, Cesare, and Parmeggiani, Alberto. "Some remarks on almost-positivity of $\psi\text{do}$'s." Bollettino dell'Unione Matematica Italiana 1-B.1 (1998): 187-215. <http://eudml.org/doc/195745>.

@article{Parenti1998,
author = {Parenti, Cesare, Parmeggiani, Alberto},
journal = {Bollettino dell'Unione Matematica Italiana},
keywords = {almost positivity; Hörmander’s inequality},
language = {eng},
month = {2},
number = {1},
pages = {187-215},
publisher = {Unione Matematica Italiana},
title = {Some remarks on almost-positivity of $\psi\text\{do\}$'s},
url = {http://eudml.org/doc/195745},
volume = {1-B},
year = {1998},
}

TY - JOUR
AU - Parenti, Cesare
AU - Parmeggiani, Alberto
TI - Some remarks on almost-positivity of $\psi\text{do}$'s
JO - Bollettino dell'Unione Matematica Italiana
DA - 1998/2//
PB - Unione Matematica Italiana
VL - 1-B
IS - 1
SP - 187
EP - 215
LA - eng
KW - almost positivity; Hörmander’s inequality
UR - http://eudml.org/doc/195745
ER -

References

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  1. BOUTET DE MONVEL, L., Hypoelliptic operators with double characteristics and related pseudo-differential operators, Comm. Pure Appl. Math., 27 (1974), 585-639. Zbl0294.35020MR370271
  2. BOUTET DE MONVEL, L.- GRIGIS, A.- HELFFER, B., Paramétrixes d'opérateurs pseudodifférentiels à caractéristiques multiples, Astérisque, 34-35 (1976), 93-121. Zbl0344.32009MR493005
  3. FEFFERMAN, C.- PHONG, D., On positivity of pseudo-differential operators, Proc. Nat. Acad. Sci. USA, 75 (1978), 4673-4674. Zbl0391.35062MR507931
  4. GÅRDING, L., Dirichlet's problem for linear elliptic partial differential equations, Math. Scand., 1 (1953), 55-72. Zbl0053.39101MR64979
  5. HELFFER, B., Invariants associés à une classe d'opérateurs pseudodifférentiels et applications à l'hypoellipticité, Ann. Inst. Fourier, 26 (1976), 55-70. Zbl0301.35026MR413199
  6. HÖRMANDER, L., Fourier integral operators, I., Acta Math., 127 (1971), 79-183. Zbl0212.46601MR388463
  7. HÖRMANDER, L., The Cauchy problem for differential equations with double characteristics, J. Anal. Math., 32 (1977), 118-196. Zbl0367.35054MR492751
  8. HÖRMANDER, L., The Analysis of Linear Partial Differential Operators, Vol.I-IV, Springer-Verlag (1983/85). Zbl0521.35002
  9. MELIN, A., Lower bounds for pseudo-differential operators, Arkiv för Matematik, 9(1971), 117-140. Zbl0211.17102MR328393
  10. MENIKOFF, A.- SJÖSTRAND, J., On the eigenvalues of a class of hypoelliptic operators, I, Math. Ann., 235 (1978), 55-85. Zbl0375.35014MR481627
  11. MOHAMED, A., Etude spectrale d'opérateurs hypoelliptiques à caractéristiques multiples, II, Communications in P.D.E., 8 (1983), 247-316. Zbl0522.35069MR692285
  12. PARENTI, C.- PARMEGGIANI, A., A necessary and sufficient condition for a lower bound for 4th-order pseudodifferential operators, J. Anal. Math., 69 (1996), 55-65. Zbl0864.35131MR1428094
  13. PARENTI, C.- PARMEGGIANI, A., Lower bounds for pseudodifferential operators, in Proceedings N.A.T.O. Conference in Microlocal Analysis and Spectral Theory, L. Rodino (ed.), Vol. 490, Kluwer Academic Publisher (1997), 251-262. Zbl0881.35132MR1451395
  14. PARMEGGIANI, A., Necessary and sufficient conditions for the almost-positivity of certain 4th-order pseudodifferential operators, to appear in Forum Mathematicum. Zbl0927.35140
  15. SHUBIN, M., Pseudodifferential Operators and Spectral Theory, Springer-Verlag (1987). Zbl0616.47040MR883081
  16. SJÖSTRAND, J., Parametrices for pseudodifferential operators with multiple characteristics, Arkiv för Matematik, 12 (1974), 85-130. Zbl0317.35076MR352749

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