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Necessary and Sufficient Conditions for Hypoellipticity for a Class of Convolution Operators
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- Journal:
- Canadian Journal of Mathematics / Volume 46 / Issue 1 / 01 February 1994
- Published online by Cambridge University Press:
- 20 November 2018, pp. 212-224
- Print publication:
- 01 February 1994
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- Article
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In this paper the Corwin's conjecture is proved, which says that if d is a function analytic near ∞, then the hypoellipticity of the convolution operator Ad, defined by
for every u ∊ S'(ℝn), implies that P(x)/ logx → ∞ as x → ∞, where P(x) is the distance from x ∊ ℝn to the set of complex zeros of d.
for every 