Abstract
This chapter outlines the underpinnings and the proof of the Fundamental Principle of Leon Ehrenpreis, according to which 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.
Mathematics Subject Classification (2010):Primary 35E20, Secondary 35C15, 35E10
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- 1.
Most of the time in the sequel the arrows indicating vector values will be omitted.
- 2.
The notations P, Q, … will always stand for matrix-valued polynomials. The corresponding differential operators will always be denoted by \(P\left (D\right )\), \(Q\left (D\right ),\ldots \)
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Treves, F. (2013). Ehrenpreis and the Fundamental Principle. In: Farkas, H., Gunning, R., Knopp, M., Taylor, B. (eds) From Fourier Analysis and Number Theory to Radon Transforms and Geometry. Developments in Mathematics, vol 28. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4075-8_24
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DOI: https://doi.org/10.1007/978-1-4614-4075-8_24
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