Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Equations with constant coefficients invariant under a group of linear transformations


Author: André Cerezo
Journal: Trans. Amer. Math. Soc. 204 (1975), 267-298
MSC: Primary 35E99; Secondary 46F15, 58G15
DOI: https://doi.org/10.1090/S0002-9947-1975-0430501-1
MathSciNet review: 0430501
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: If $ P$ is a linear differential operator on $ {{\mathbf{R}}^n}$ with constant coefficients, which is invariant under a group $ G$ of linear transformations, it is not true in general that the equation $ Pu = f$ always has a $ G$-invariant solution $ u$ for a $ G$-invariant $ f$. We elucidate here the particular case of a ``big'' group $ G$, and we count the invariant solutions when they exist (see Corollary 28 and Theorems 32, 33). The case, of special interest, of the wave equation and the Lorentz group is covered (Corollary 27). The theory of hyperfunctions provides the frame for the work.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35E99, 46F15, 58G15

Retrieve articles in all journals with MSC: 35E99, 46F15, 58G15


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1975-0430501-1
Article copyright: © Copyright 1975 American Mathematical Society