Some remarks on almost-positivity of ψdo's
Parenti, Cesare ; Parmeggiani, Alberto
Bollettino dell'Unione Matematica Italiana, Tome 1-A (1998), p. 187-215 / Harvested from Biblioteca Digitale Italiana di Matematica

Per una classe di operatori pseudodifferenziali a caratteristiche multiple vengono date condizioni necessarie e sufficienti per la validità di stime dal basso «ottimali»

Publié le : 1998-02-01
@article{BUMI_1998_8_1B_1_187_0,
     author = {Cesare Parenti and Alberto Parmeggiani},
     title = {Some remarks on almost-positivity of $\psi\text{do}$'s},
     journal = {Bollettino dell'Unione Matematica Italiana},
     volume = {1-A},
     year = {1998},
     pages = {187-215},
     zbl = {0908.35146},
     mrnumber = {1618980},
     language = {en},
     url = {http://dml.mathdoc.fr/item/BUMI_1998_8_1B_1_187_0}
}
Parenti, Cesare; Parmeggiani, Alberto. Some remarks on almost-positivity of $\psi\text{do}$'s. Bollettino dell'Unione Matematica Italiana, Tome 1-A (1998) pp. 187-215. http://gdmltest.u-ga.fr/item/BUMI_1998_8_1B_1_187_0/

[1] Boutet De Monvel, L., Hypoelliptic operators with double characteristics and related pseudo-differential operators, Comm. Pure Appl. Math., 27 (1974), 585-639. | MR 370271 | Zbl 0294.35020

[2] Boutet De Monvel, L.-Grigis, A.-Helffer, B., Paramétrixes d'opérateurs pseudodifférentiels à caractéristiques multiples, Astérisque, 34-35 (1976), 93-121. | MR 493005 | Zbl 0344.32009

[3] Fefferman, C.-Phong, D., On positivity of pseudo-differential operators, Proc. Nat. Acad. Sci. USA, 75 (1978), 4673-4674. | MR 507931 | Zbl 0391.35062

[4] Gårding, L., Dirichlet's problem for linear elliptic partial differential equations, Math. Scand., 1 (1953), 55-72. | MR 64979 | Zbl 0053.39101

[5] Helffer, B., Invariants associés à une classe d'opérateurs pseudodifférentiels et applications à l'hypoellipticité, Ann. Inst. Fourier, 26 (1976), 55-70. | MR 413199 | Zbl 0301.35026

[6] Hörmander, L., Fourier integral operators, I., Acta Math., 127 (1971), 79-183. | MR 388463 | Zbl 0212.46601

[7] Hörmander, L., The Cauchy problem for differential equations with double characteristics, J. Anal. Math., 32 (1977), 118-196. | MR 492751 | Zbl 0367.35054

[8] Hörmander, L., The Analysis of Linear Partial Differential Operators, Vol.I-IV, Springer-Verlag (1983/85). | Zbl 0521.35002

[9] Melin, A., Lower bounds for pseudo-differential operators, Arkiv för Matematik, 9(1971), 117-140. | MR 328393 | Zbl 0211.17102

[10] Menikoff, A.-Sjöstrand, J., On the eigenvalues of a class of hypoelliptic operators, I, Math. Ann., 235 (1978), 55-85. | MR 481627 | Zbl 0375.35014

[11] Mohamed, A., Etude spectrale d'opérateurs hypoelliptiques à caractéristiques multiples, II, Communications in P.D.E., 8 (1983), 247-316. | MR 692285 | Zbl 0522.35069

[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. | MR 1428094 | Zbl 0864.35131

[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. | MR 1451395 | Zbl 0881.35132

[14] Parmeggiani, A., Necessary and sufficient conditions for the almost-positivity of certain 4th-order pseudodifferential operators, to appear in Forum Mathematicum. | Zbl 0927.35140

[15] Shubin, M., Pseudodifferential Operators and Spectral Theory, Springer-Verlag (1987). | MR 883081 | Zbl 0616.47040

[16] Sjöstrand, J., Parametrices for pseudodifferential operators with multiple characteristics, Arkiv för Matematik, 12 (1974), 85-130. | MR 352749 | Zbl 0317.35076