Abstract
In this work we discuss the problem of smooth and analytic regularity for hyperfunction solutions to linear partial differential equations with analytic coefficients. In particular we show that some well known “sum of squares” operators, which satisfy Hörmander’s condition and consequently are hypoelliptic, admit hyperfunction solutions that are not smooth (in particular they are not distributions).
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This research project was supported by the NSF Grant INT 0227100. P. D. Cordaro was also partially supported by CNPq and Fapesp.
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Cordaro, P.D., Hanges, N. Hyperfunctions and (analytic) hypoellipticity. Math. Ann. 344, 329–339 (2009). https://doi.org/10.1007/s00208-008-0308-2
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DOI: https://doi.org/10.1007/s00208-008-0308-2