Abstract
This chapter contains the most classical result on Carleman Inequalities, due to L. Hörmander, who introduced the notion of hypersurface strongly pseudo-convex with respect to an operator, a condition taking into account the “shape” and orientation of an hypersurface with respect to the bicharacteristic flow of the principal symbol of the operator under scope.
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Notes
- 1.
The Cauchy–Schwarz inequality, also known as the Cauchy–Bunyakovsky–Schwarz inequality, was stated and proven in the course of the nineteenth century. The German mathematician Hermann Amandus Schwarz (1843–1921) should not be confused with Laurent Schwartz (1915–2002), a French mathematician, the creator of the modern Theory of Distributions.
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Lerner, N. (2019). Pseudo-convexity: Hörmander’s Theorems. In: Carleman Inequalities. Grundlehren der mathematischen Wissenschaften, vol 353. Springer, Cham. https://doi.org/10.1007/978-3-030-15993-1_4
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DOI: https://doi.org/10.1007/978-3-030-15993-1_4
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