Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Singular solutions for a class
of Grusin type operators


Authors: Nicholas Hanges and A. Alexandrou Himonas
Journal: Proc. Amer. Math. Soc. 124 (1996), 1549-1557
MSC (1991): Primary 35H05
MathSciNet review: 1307525
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

  • 1. Louis Boutet de Monvel and François Trèves, On a class of pseudodifferential operators with double characteristics, Invent. Math. 24 (1974), 1–34. MR 0353064
  • 2. 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 0437961
  • 3. Antonio Gilioli and François Trèves, An example in the solvability theory of linear PDE’s, Amer. J. Math. 96 (1974), 367–385. MR 0355285
  • 4. V. V. Grušin, A certain class of hypoelliptic operators, Mat. Sb. (N.S.) 83 (125) (1970), 456–473 (Russian). MR 0279436
  • 5. Lars Hörmander, A class of hypoelliptic pseudodifferential operators with double characteristics, Math. Ann. 217 (1975), no. 2, 165–188. MR 0377603
  • 6. Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 0222474
  • 7. Lars Hörmander, The analysis of linear partial differential operators. IV, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 275, Springer-Verlag, Berlin, 1985. Fourier integral operators. MR 781537
  • 8. 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
  • 9. 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
  • 10. Linda Preiss Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), no. 3-4, 247–320. MR 0436223
  • 11. Gabor Szegö, Orthogonal polynomials, American Mathematical Society Colloquium Publications, Vol. 23. Revised ed, American Mathematical Society, Providence, R.I., 1959. MR 0106295

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 35H05

Retrieve articles in all journals with MSC (1991): 35H05


Additional Information

Nicholas Hanges
Affiliation: Department of Mathematics, Herbert H. Lehman College-CUNY, Bronx, New York 10468-1589
Email: nwhlc@cunyvm.cuny.edu

A. Alexandrou Himonas
Affiliation: Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556
Email: Alex.A.Himonas.1@nd.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-96-03180-2
Keywords: Eigenvalue, eigenfunction, concatenations, hypoellipticity, double characteristics
Received by editor(s): October 14, 1994
Received by editor(s) in revised form: November 14, 1994
Additional Notes: The first author was partially supported by NSF Grant DMS 91-04569.
The second author was partially supported by NSF Grant DMS 91-01161.
Communicated by: Jeffrey Rauch
Article copyright: © Copyright 1996 American Mathematical Society