Bégout, Pascal (2022) The dual space of a complex Banach space restricted to the field of real numbers. Advances in mathematical sciences and applications, vol. 31 (n° 2). pp. 241-252.

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Solutions of some partial differential equations are obtained as critical points of a real funtional. Then the Banach space where this functional is defined has to be real, otherwise, it is not differentiable. It follows that the equation is solved with respect to the real dual space of this Banach space. But if the solution is complex-valued there is the following problem: what does the multiplication of this equation by a complex number mean~? In this note, we explain how to rigorously define this operation.

Item Type: Article
Language: English
Date: 2022
Refereed: Yes
Place of Publication: Tokyo
Uncontrolled Keywords: Dual space, Differentiability
Keywords (French): Espace dual, Différentiabilité
Divisions: Institut de mathématiques de Toulouse
Site: UT1
Date Deposited: 01 Jul 2022 10:04
Last Modified: 01 Jul 2022 10:04
URI: https://publications.ut-capitole.fr/id/eprint/45662
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