Elementary proofs of analytic hypoellipticity for $\square_b$ and the $\overline \partial$

Elementary proofs of analytic hypoellipticity for

□_{b}

and the

\bar{\partial}

- Neumann problem

Tartakoff, D. S.

Analytic solutions of partial differential equations - Trento, 1981, Astérisque no. 89-90 (1981), p. 85-116

MR 666404 | Zbl 0497.35023

@incollection{AST_1981__89-90__85_0,
     author = {Tartakoff, D. S.},
     title = {Elementary proofs of analytic hypoellipticity for $\square\_b$ and the $\overline \partial$ - Neumann problem},
     booktitle = {Analytic solutions of partial differential equations - Trento, 1981},
     author = {Collectif},
     series = {Ast\'erisque},
     publisher = {Soci\'et\'e math\'ematique de France},
     number = {89-90},
     year = {1981},
     pages = {85-116},
     zbl = {0497.35023},
     mrnumber = {666404},
     language = {en},
     url = {http://www.numdam.org/item/AST_1981__89-90__85_0}
}

Tartakoff, D. S. Elementary proofs of analytic hypoellipticity for $\square_b$ and the $\overline \partial$ - Neumann problem, in Analytic solutions of partial differential equations - Trento, 1981, Astérisque, no. 89-90 (1981), pp. 85-116. http://www.numdam.org/item/AST_1981__89-90__85_0/

References

[1] K. G. Anderson, Propagation of analyticity of solutions of partial differential équations with constant coefficients, Ark for Matematik, 8 (1970), pp. 277-302. | Article | MR 299938 | Zbl 0211.40502

[2] M. S. Baouendi and C. Goulaouic, Non analytic-hypoellipticity for some degenerate operators, Bull. Amer. Math. Soc. 78 (1972), p. 483. | Article | MR 296507 | Zbl 0276.35023

[3] R. Beals, Séminaire Goulaouic-Schwartz 1976-77, exposé 19.

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

[5] L. Boutet De Monvel and P. Kree, Pseudo-differential operators and Gevrey classes, Ann. Inst. Fourier Grenoble, 17 (1967), pp. 295-323. | Article | MR 226170 | Zbl 0195.14403

[6] L. Corwin and L. P. Rothschild, Necessary conditions for local solvability of homogeneous left invariant differential operators on nilpotent groups, (preprint). | Article | MR 639041 | Zbl 0486.22006

[7] P. Greiner, J. J. Kohn and E. Stein, Necessary and sufficient conditions for solvability of the Lewy équation, Proc. Nat. Acad. Sci. U.S.A. 72 (1975), pp. 3287-3289. | Article | MR 380142 | Zbl 0308.35017

[8] B. Helffer and J. Nourrigat, Hypoellipticité pour des groupes nilpotents de rang de nilpotence 3, Comm. in P.D.E., III (8) (1978), pp. 643-743. | Article | MR 499352 | Zbl 0385.35015

[9] D. Geller, Local solvability and homogeneous distributions on the Heisenberg group, Comm. in P.D.E. V (5) (1980), pp. 475-560. | Article | MR 571049 | Zbl 0488.22020

[10] G. Métivier, Une classe d'opérateurs non hypoélliptiques analytiques, Indiana J. of Math., (to appear). | MR 589650 | Zbl 0455.35041

[11] G. Métivier, Analytic hypoellipticity for operators with multiple characteristics, Comm. in P.D.E., VI (I) 1981, pp. 1-90. | MR 597752 | Zbl 0455.35040

[12] M. Sato, T. Kawai and M. Kashiwara, Hyperfunctions and pseudodifferential équations, Lect. Notes in Math., 287 (1973) Springer, pp. 265-529. | MR 420735 | Zbl 0277.46039

[13] J. Sjostrand, Parametrices for pseudodifferential operators with multiple characteristics, Arkiv för Mat. 12 (1974), Bibliography (cont'd). | Article | MR 352749 | Zbl 0317.35076

[14] D. S. Tartakoff, Gevrey hypoellipticity for subelliptic boundary value problems, Comm. Pure Appl. Math., 26 (1973), pp. 251-312. | Article | MR 342842 | Zbl 0265.35023

[15] D. S. Tartakoff, Local Gevrey and quasianalytic hypoellipticity for $□_{b}$ , Bull. Amer. Math. Soc, 82 (1976), pp. 740-742. | Article | MR 410810 | Zbl 0331.35017

[16] D. S. Tartakoff, Local analytic hypoellipticity for $□_{b}$ on nondegenerate Cauchy-Riemann manifolds, Proc. Nat. Acad. Sci. U.S.A., 75 (1978), pp. 3027-3028. | Article | MR 499657 | Zbl 0384.35020

[17] D. S. Tartakoff, The local real analyticity of solutions to $□_{b}$ and the $\bar{\partial}$ -Neumann problem, Acta Math., 145 (1980), pp. 177-204. | Article | MR 590289 | Zbl 0456.35019

[18] F. Trèves, Analytic hypoellipticity of a class of pseudo-differential operators, Comm. in Partial Diff. Equ. 3 (1978), pp. 475-642. | Zbl 0384.35055