Ehrenpreis's fundamental principle

In mathematical analysis, Ehrenpreis's fundamental principle, introduced by Leon Ehrenpreis, states:^[1]

Every solution of a system (in general, overdetermined) of homogeneous partial differential equations with constant coefficients can be represented as the integral with respect to an appropriate Radon measure over the complex “characteristic variety” of the system.^[2]

References

^ Treves, François (2013). "Ehrenpreis and the Fundamental Principle". From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics. Vol. 28. pp. 491–507. doi:10.1007/978-1-4614-4075-8_24. ISBN 978-1-4614-4074-1.
^ Oshima, Toshio (1974). "A Proof of Ehrenpreis' Fundamental Principle in Hyperfunctions". Proceedings of the Japan Academy. 50: 16–18. doi:10.3792/pja/1195519103. Retrieved 25 July 2013.

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[1] Treves, François (2013). "Ehrenpreis and the Fundamental Principle". From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics. Vol. 28. pp. 491–507. doi:10.1007/978-1-4614-4075-8_24. ISBN 978-1-4614-4074-1.

[2] Oshima, Toshio (1974). "A Proof of Ehrenpreis' Fundamental Principle in Hyperfunctions". Proceedings of the Japan Academy. 50: 16–18. doi:10.3792/pja/1195519103. Retrieved 25 July 2013.

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