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Remarks On Convexity With Respect To Operators Of Real Principal Type

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Abstract

P-convexity with respect to singular supports has been completely characterized in geometrical terms when P is an operator of principal type. (See [2, section 1.4].) However, no satisfactory geometrical interpretation of P-convexity (with respect to supports) is known even when P is of real principal type as we shall assume throughout this paper.

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References

  • [1] L. Hörmander, Linear partial differential operators, Springer-Verlag, Berlin-Göttingen-Heidelberg, 1963.

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  • [2] L. Hörmander, On the existence and regularity of solutions of linear pseudo-differential equations, Ens. Math. 17 (1971), 99–163.

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  • [3] L. Hörmander Uniqueness theorems and wave front sets for solutions of linear differential equations with analytic coefficients, Comm. Pure Appl. Math. 24 (1971), 671–704.

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  • [4] B. Malgrange, Sur les ouverts convexes par rapport Ă  un opĂ©rateur diffĂ©rentiel, C. R. Acad. Sci. Paris 254 (1962), 614–615.

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  • [5] F. Treves, Linear partial differential equations with constant coefficients, Gordon and Breach, New York, 1966.

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  • [6] E.C. Zachmanoglou, Non-uniqueness of the Cauchy problem for linear partial differential equations with variable coefficients, Arch. Rat. Mech. Anal. 27 (1968), 373–384.

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Correspondence to Lars Hörmander .

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Hörmander, L. (2018). Remarks On Convexity With Respect To Operators Of Real Principal Type. In: Unpublished Manuscripts . Springer, Cham. https://doi.org/10.1007/978-3-319-69850-2_15

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