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Necessary and Sufficient Conditions for Hypoellipticity for a Class of Convolution Operators

Published online by Cambridge University Press:  20 November 2018

Luo Xuebo
Luo Xuebo*
Affiliation:
Department of Mathematics Lanzhou University Lanzhou 730000 China
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Abstract

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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.

Keywords

35H2522E27
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 46 , Issue 1 , 01 February 1994 , pp. 212 - 224
Copyright
Copyright © Canadian Mathematical Society 1994

Footnotes

Supported by NNFC and Special Fund for Doctoral Program in University.

References

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3. Narasimhan, R., Several Complex Variables, The University of Chicago Press, Chicago and London, 1971.Google Scholar
4. Porter, M. H. and Weinberger, H. F., Maximum Principles in Differential Equations, Prentice-Hall, Englewood Cliffs, New Jersey, 1967.Google Scholar
5. Barros-Neto, J., An Introduction to the Theory of Distributions, Marcel Dekker, New York, 1973.Google Scholar