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Fundamental solutions for hypoelliptic differential operators depending analytically on a parameter


Author: Frank Mantlik
Journal: Trans. Amer. Math. Soc. 334 (1992), 245-257
MSC: Primary 35H05; Secondary 35B30
DOI: https://doi.org/10.1090/S0002-9947-1992-1107027-5
MathSciNet review: 1107027
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Abstract: Let $ P(\lambda ,D) = \sum\nolimits_{\vert\alpha \vert \leq m} {{a_\alpha }(\lambda ){D^\alpha }} $ be a differential operator with constant coefficients $ {a_\alpha }$ depending analytically on a parameter $ \lambda $. Assume that each $ P(\lambda ,D)$ is hypoelliptic and that the strength of $ P(\lambda ,D)$ is independent of $ \lambda $. Under this condition we show that there exists a regular fundamental solution of $ P(\lambda ,D)$ which also depends analytically on $ \lambda $.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1107027-5
Keywords: Hypoelliptic operators, fundamental solutions, analytic parameterdependence
Article copyright: © Copyright 1992 American Mathematical Society

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