Published in Transactions of the American Mathematical Society, Volume 348, Issue 2, February 1, 1996, pages 673-689.
This article was first published in Transactions of the American Mathematical Society, published by the American Mathematical Society. Copyright © 1996 American Mathematical Society.
We prove the existence of solutions for essentially all linear partial differential equations with C∞-coefficients in an algebra of generalized functions, defined in the paper. In particular, we show that H. Lewy’s equation has solutions whenever its right-hand side is a classical C∞-function.