On a class of unsolvable operators

Massimo Cicognani; Luisa Zanghirati

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1993)

  • Volume: 20, Issue: 3, page 357-369
  • ISSN: 0391-173X

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Cicognani, Massimo, and Zanghirati, Luisa. "On a class of unsolvable operators." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 20.3 (1993): 357-369. <http://eudml.org/doc/84153>.

@article{Cicognani1993,
author = {Cicognani, Massimo, Zanghirati, Luisa},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {microlocal solutions; microlocal solution; analytic pseudodifferential operator of complex principle type; Mizohata operator; analytic-Gevrey hypoellipticity problem; operators with multiple characteristics; Gevrey class; microanalytic terms; analytic Gevrey hypoellipticity},
language = {eng},
number = {3},
pages = {357-369},
publisher = {Scuola normale superiore},
title = {On a class of unsolvable operators},
url = {http://eudml.org/doc/84153},
volume = {20},
year = {1993},
}

TY - JOUR
AU - Cicognani, Massimo
AU - Zanghirati, Luisa
TI - On a class of unsolvable operators
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1993
PB - Scuola normale superiore
VL - 20
IS - 3
SP - 357
EP - 369
LA - eng
KW - microlocal solutions; microlocal solution; analytic pseudodifferential operator of complex principle type; Mizohata operator; analytic-Gevrey hypoellipticity problem; operators with multiple characteristics; Gevrey class; microanalytic terms; analytic Gevrey hypoellipticity
UR - http://eudml.org/doc/84153
ER -

References

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  1. [1] F. Cardoso, A necessary condition of Gevrey solvability for differential operators with double characteristics. Comm. Partial Differential Equations, 14 (1989), 981-1009. Zbl0719.35001MR1017059
  2. [2] F. Cardoso - F. Treves, A necessary condition of local solvability for pseudodifferential equations with double characteristics. Ann. Inst. Fourier (Grenoble), 24:1 (1974), 225-292. Zbl0273.35058MR350233
  3. [3] L. Cattabriga - L. Rodino - L. Zanghirati, Analytic-Gevrey hypoellipticity for a class of pseudodifferential operators with multiple characteristics. Comm. Partial Differential Equations, 15 (1989), 81-96. Zbl0704.35035MR1032624
  4. [4] L. Cattabriga - L. Zanghirati, Fourier integral operators of infinite order on Gevrey spaces. Applications to the Cauchy problem for certain hyperbolic operators. J. Math. Kyoto Univ., 30 (1990), 149-192. Zbl0725.35113MR1041717
  5. [5] J.J. Duistermaat - J. Sjöstrand, A global construction for pseudo-differential operators with non-involutive characteristics. Invent. Math., 20 (1973), 209-225. Zbl0282.35071MR344942
  6. [6] Y. Egorov, On necessary conditions for local solvability of pseudodifferential equations of principal type. Trudy Moskov. Mat. Obshch., 24 (1971), 24-42 (Russian); Trans. Moscow Math. Soc., 24 (1971), 632-635. Zbl0296.35071
  7. [7] R. Goldman, A necessary condition for local solvability of a pseudodifferential equation having multiple characteristics. J. Differential Equations, 19 (1975), 176-200. Zbl0305.35085MR380171
  8. [8] T. Gramchev, Non solvability for analytic partial differential operators with multiple complex characteristic. To appear. 
  9. [9] T. Gramchev, Powers of Mizohata type operators in Gevrey classes. Boll. Un. Mat. Ital. B (7) 1, 1991. Zbl0809.47043MR1110672
  10. [10] V.V. Grušin, On a class of elliptic pseudo differential operators degenerate on a submanifold. Mat. Sb., 84 (1977), 163-195; Math. USSR-Sb., 13 (1971), 155-185. MR283630
  11. [11] N. Hanges, Almost Mizohata operators. Trans. Amer. Math. Soc., 293 (1986), 663-675. Zbl0606.35010MR816318
  12. [12] L. Hörmander, The analysis of linear partial differential operators, Voll. I-IV. Springer-Verlag, Berlin, 1983-85. Zbl0521.35002
  13. [13] H. Komatsu, Ultradistributions I, structure theorems and a characterization, J. Fac. Sci. Univ. Tokyo, Sect. IA Math., 20 (1973), 25-105. Zbl0258.46039MR320743
  14. [14] H. Ninomiya, Necessary and sufficient conditions for the local solvability of the Mizohata equations. J. Math. Kyoto Univ., 28:4 (1988), 593-603. Zbl0692.35026MR981095
  15. [15] L. Nirenberg - F. Treves, On local solvability of linear partial differential equations, I-Necessary conditions. Comm. Pure Appl. Math., 23 (1970), 1-38. Zbl0191.39103MR264470
  16. [16] P. Popivanov, On the local solvability of a class of partial differential equations with double characteristics. Trudy Sem. Petrovsk.1, (1975), 237-278 (Russian); Amer. Math. Soc. Transl., 118:2 (1982), 51-89. Zbl0495.35083MR427811
  17. [17] L. Rodino - A. Corli, Gevrey solvability for hyperbolic operators with constant multiplicity. Recent developments in hyperbolic equations, Proc. of Conference "Hyperbolic Equations" - Pisa1987, LongmanHarlow, 1988. Zbl0739.35002MR984375
  18. [18] L. Rodino - L. Zanghirati, Pseudodifferential operators with multiple characteristics, and Gevrey singularities, Comm. Partial Differential Equations, 11 (1986), 673-711. Zbl0597.58034MR837927
  19. [19] F. Treves, Introduction to pseudodifferential and Fourier integral operators, Vol. I, Plenum Press, New York, 1980. Zbl0453.47027MR597145
  20. [20] F. Treves, Remarks about certain first order linear PDE in two variables. Comm. Partial Differential Equations, 5 (1980), 381-425. Zbl0519.35008MR567779
  21. [21] L. Zanghirati, Pseudodifferential operators of infinite order and Gevrey classes, Ann. Univ. Ferrara, Sez. VII, Sc. Mat., 31 (1985), 197-219. Zbl0601.35110MR841860

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