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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
DOI: https://doi.org/10.1090/S0002-9939-96-03180-2
MathSciNet review: 1307525
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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. L. Boutet de Monvel and F. Treves, On a class of pseudodifferential equations with double characteristics, Inventiones Math. 24 (1974), 1-34. MR 50:5550
  • 2. A. Gilioli, A class of second-order evolution equations with double characteristics, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 4, no. 3 (1976), 187-229. MR 55:10882
  • 3. A. Gilioli and F. Treves, An example in the local solvability theory of linear PDE's, American Journal of Math. 24, No. 2 (1974), 366-384. MR 50:7761
  • 4. V. V. Grusin, On a class of hypoelliptic operators, Math. Sbornik. 83, No. 125 (1970), 456-473. MR 43:5158
  • 5. L. Hörmander, A class of hypoelliptic pseudo-differential operators with double characteristics, Math. Ann. 217 (1975), 165-188. MR 51:13774
  • 6. L. Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147-171. MR 36:5526
  • 7. L. Hörmander, The Analysis of Linear Partial Differential Operators, vol. I-IV, Springer-Verlag, Grundlehren der Mathematischen Wissenschften, 1984. MR 87d:35002b
  • 8. J.J. Kohn, Pseudo-differential operators and hypoellipticity, Proceedings of symposia in pure mathematics XXIII (1973), 61-70. MR 49:3356
  • 9. O. A. Oleinik and E. V. Radkevic, Second order equations with nonnegative characteristic form, AMS and Plenum Press, 1973. MR 56:16112
  • 10. L.P. Rothschild and E.M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1977), 247-320. MR 55:9171
  • 11. G. Szegö, Orthogonal Polynomials, American Mathematical Society, 1959. MR 21:5029

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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: https://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

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