On the Holonomic Character of the Elementary Solution of a Partial Differential Operator

Louis Boutet de Monvel
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Louis Boutet de Monvel: Université Pierre et Marie Curie, Institut de Mathématiques, Analyse Algébrique

A chapter in New Trends in Microlocal Analysis, 1997, pp 171-177 from Springer

Abstract: Abstract We describe an elementary regular holonomic system of partial differential equations which should be satisfied by an elementary solution of a differential operator P(d) with constant coefficients and simple characteristics. This is heuristic, but it is exact for strictly hyperbolic operators, and exact mod. holomorphic functions for elliptic operators or operators with real principal part. For these this explains again why the elementary solution extends holomorphically, with the expected ramification

Keywords: Differential Operator; Elementary Solution; Principal Part; Zero Section; Simple Characteristic (search for similar items in EconPapers)
Date: 1997
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-4-431-68413-8_14

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DOI: 10.1007/978-4-431-68413-8_14

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