Singular solutions for a class of Grusin type operators

Hanges, Nicholas; Himonas, A.

doi:10.1090/S0002-9939-96-03180-2

Singular solutions for a class of Grusin type operators
HTML articles powered by AMS MathViewer

by Nicholas Hanges and A. Alexandrou Himonas PDF

Proc. Amer. Math. Soc. 124 (1996), 1549-1557 Request permission

Abstract:

We construct singular solutions for a one-parameter family of partial differential equations with double characteristics and with complex lower order terms. The parameter belongs to a discrete set which is described in terms of the spectrum of a related differential operator.

References

Louis Boutet de Monvel and François Trèves, On a class of pseudodifferential operators with double characteristics, Invent. Math. 24 (1974), 1–34. MR 353064, DOI 10.1007/BF01418785
Antonio Gilioli, A class of second-order evolution equations with double characteristics, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 3 (1976), no. 2, 187–229. MR 437961
Antonio Gilioli and François Trèves, An example in the solvability theory of linear PDE’s, Amer. J. Math. 96 (1974), 367–385. MR 355285, DOI 10.2307/2373639
V. V. Grušin, A certain class of hypoelliptic operators, Mat. Sb. (N.S.) 83 (125) (1970), 456–473 (Russian). MR 0279436
Lars Hörmander, A class of hypoelliptic pseudodifferential operators with double characteristics, Math. Ann. 217 (1975), no. 2, 165–188. MR 377603, DOI 10.1007/BF01351297
Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI 10.1007/BF02392081
Lars Hörmander, The analysis of linear partial differential operators. III, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 274, Springer-Verlag, Berlin, 1985. Pseudodifferential operators. MR 781536
J. J. Kohn, Pseudo-differential operators and hypoellipticity, Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971) Amer. Math. Soc., Providence, R.I., 1973, pp. 61–69. MR 0338592
O. A. Oleĭnik and E. V. Radkevič, Second order equations with nonnegative characteristic form, Plenum Press, New York-London, 1973. Translated from the Russian by Paul C. Fife. MR 0457908, DOI 10.1007/978-1-4684-8965-1
Linda Preiss Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), no. 3-4, 247–320. MR 436223, DOI 10.1007/BF02392419
Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23, American Mathematical Society, Providence, R.I., 1959. Revised ed. MR 0106295