Solvability of linear systems of PDE’s with constant coefficients
HTML articles powered by AMS MathViewer
- by Ding-Xuan Zhou PDF
- Proc. Amer. Math. Soc. 127 (1999), 2013-2017 Request permission
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.References
- Wolfgang Dahmen and Charles A. Micchelli, On multivariate $E$-splines, Adv. Math. 76 (1989), no. 1, 33–93. MR 1004486, DOI 10.1016/0001-8708(89)90043-1
- Wolfgang Dahmen and Charles A. Micchelli, Local dimension of piecewise polynomial spaces, syzygies, and solutions of systems of partial differential equations, Math. Nachr. 148 (1990), 117–136. MR 1127336, DOI 10.1002/mana.3211480107
- Leon Ehrenpreis, Fourier analysis in several complex variables, Pure and Applied Mathematics, Vol. XVII, Wiley-Interscience [A division of John Wiley & Sons, Inc.], New York-London-Sydney, 1970. MR 0285849
- Rong Qing Jia, The Toeplitz theorem and its applications to approximation theory and linear PDEs, Trans. Amer. Math. Soc. 347 (1995), no. 7, 2585–2594. MR 1277117, DOI 10.1090/S0002-9947-1995-1277117-8
- R. Q. Jia, Shift-Invariant spaces and linear operator equations, Israel J. Math. 103 (1998), 259–288.
- Rong Qing Jia, Sherman Riemenschneider, and Zuowei Shen, Solvability of systems of linear operator equations, Proc. Amer. Math. Soc. 120 (1994), no. 3, 815–824. MR 1169033, DOI 10.1090/S0002-9939-1994-1169033-1
- U. Oberst, Variations on the fundamental principle for linear systems of partial differential and difference equations with constant coefficients, preprint.
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
- Received by editor(s): October 25, 1995
- Received by editor(s) in revised form: September 15, 1997
- Published electronically: 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 1999 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 127 (1999), 2013-2017
- MSC (1991): Primary 35A99, 41A15, 41A63
- DOI: https://doi.org/10.1090/S0002-9939-99-04713-9
- MathSciNet review: 1476403