## Systems of partial differential operators with fundamental solutions supported by a cone

HTML articles powered by AMS MathViewer

- by Kirk E. Lancaster and Bent E. Petersen PDF
- Proc. Amer. Math. Soc.
**78**(1980), 247-252 Request permission

## Abstract:

Necessary and sufficient conditions are given for a system of partial differential operators to have a fundamental solution supported by a convex salient cone. As a simple application an overdetermined Cauchy problem is solved.## References

- M. F. Atiyah, R. Bott, and L. Gȧrding,
*Lacunas for hyperbolic differential operators with constant coefficients. I*, Acta Math.**124**(1970), 109–189. MR**470499**, DOI 10.1007/BF02394570
W. F. Donoghue, Jr., - Arne Enqvist,
*On fundamental solutions supported by a convex cone*, Ark. Mat.**12**(1974), 1–40. MR**344657**, DOI 10.1007/BF02384744 - Arne Enqvist,
*On temperate fundamental solutions supported by a convex cone*, Ark. Mat.**14**(1976), no. 1, 35–41. MR**422840**, DOI 10.1007/BF02385821
L. Hörmander, - Lars Hörmander,
*An introduction to complex analysis in several variables*, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1966. MR**0203075** - Bent E. Petersen,
*On the Laplace transform of a temperate distribution supported by a cone*, Proc. Amer. Math. Soc.**35**(1972), 123–128. MR**298414**, DOI 10.1090/S0002-9939-1972-0298414-9 - Bent E. Petersen,
*Holomorphic functions with growth conditions*, Trans. Amer. Math. Soc.**206**(1975), 395–406. MR**379879**, DOI 10.1090/S0002-9947-1975-0379879-8 - B. E. Petersen,
*Holomorphic functions with bounds*, Complex analysis and its applications (Lectures, Internat. Sem., Trieste, 1975) Internat. Atomic Energy Agency, Vienna, 1976, pp. 107–120. MR**0477148** - Laurent Schwartz,
*Théorie des distributions*, Publications de l’Institut de Mathématique de l’Université de Strasbourg, IX-X, Hermann, Paris, 1966 (French). Nouvelle édition, entiérement corrigée, refondue et augmentée. MR**0209834** - K. T. Smith,
*Formulas to represent functions by their derivatives*, Math. Ann.**188**(1970), 53–77. MR**282046**, DOI 10.1007/BF01435415

*Distributions and Fourier transforms*, Academic Press, New York, 1969.

*Linear partial differential operators*, Springer-Verlag, Berlin, 1963.

## Additional Information

- © Copyright 1980 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**78**(1980), 247-252 - MSC: Primary 35L55; Secondary 35E15, 58G16
- DOI: https://doi.org/10.1090/S0002-9939-1980-0550506-7
- MathSciNet review: 550506