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Space of Solutions of Homogeneous Elliptic Equations

Published online by Cambridge University Press:  20 November 2018

E. Dubinsky  and
T. Husain
E. Dubinsky
Affiliation:
Mcmaster University, Hamilton, Ontario
T. Husain
Affiliation:
Mcmaster University, Hamilton, Ontario
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This is the continuation of our paper [1] and includes the results promised there. As in [1], we consider a homogeneous elliptic equation in two variables. In [1] we showed that all solutions of such equations can be written in a specific form, viz. in the form of an infinite series in certain specific polynomials. Here we first establish that a common solution of any two positive powers of any two linearly independent, linear elliptic polynomials can be expressed as a polynomial (Lemma 2).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 14 , Issue 1 , January 1971 , pp. 17 - 24
Copyright
Copyright © Canadian Mathematical Society 1971

References

1. Dubinsky, E. and Husain, T., Solutions of homogeneous elliptic equations, Canad. Math. Bull. 13 (1970), 99-106.Google Scholar
2. Pietsch, A., Nukleare lokalkonvexe Raurne, Berlin, 1965.Google Scholar
3. Sĭlov, G. E., Local properties of solutions of partial differential equations with constant coefficients, Trans. Amer. Math. Soc. (Series 2) 42 (1964), 129-173.Google Scholar