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Solvability of linear systems of PDE's with constant coefficients
Author(s):
Ding-Xuan
Zhou
Journal:
Proc. Amer. Math. Soc.
127
(1999),
2013-2017.
MSC (1991):
Primary 35A99, 41A15, 41A63
Posted:
March 1, 1999
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Abstract:
In this paper we investigate the solvability of linear systems of partial differential equations with constant coefficients in a field of positive characteristic. In particular, we prove that consistence and compatibility are equivalent, which answers a question of Ehrenpreis and extends a result of Jia. The problem of uniqueness is also considered.
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- 3.
- L. Ehrenpreis, Fourier Analysis in Several Complex Variables, Tracts in Mathematics 17, Wiley-Interscience Publishers (1970), New York. MR 44:3066
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- R. Q. Jia, The Toeplitz theorem and its applications to approximation theory and linear PDE's, Trans. Amer. Math. Soc. 347(1995), 2585-2594. MR 95i:41014
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- R. Q. Jia, Shift-Invariant spaces and linear operator equations, Israel J. Math. 103 (1998), 259-288. CMP 98:10
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Additional Information:
Ding-Xuan
Zhou
Affiliation:
Department of Mathematics, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong
Email:
mazhou@math.cityu.edu.hk
DOI:
10.1090/S0002-9939-99-04713-9
PII:
S 0002-9939(99)04713-9
Keywords:
Linear systems of partial differential equations,
positive characteristic,
consistence,
compatibility
Received by editor(s):
October 25, 1995
Received by editor(s) in revised form:
September 15, 1997
Posted:
March 1, 1999
Additional Notes:
The author is supported in part by Research Grants Council and City University of Hong Kong under Grants \#9040281, 9030562, 7000741. This research was done while visiting the University of Alberta, Canada.
Communicated by:
J. Marshall Ash
Copyright of article:
Copyright
1999,
American Mathematical Society
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