Duality by reproducing kernels


Тип публикации: статья из журнала

Год издания: 2003

Идентификатор DOI: 10.1155/S0161171203206037

Аннотация: Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X. Write 𝒮A (𝒟) for the space of solutions of the system Au=0 in a domain 𝒟?X. Using reproducing kernels related to various Hubert structures on subspaces of 𝒮A (𝒟), we show explicit identifications of the duПоказать полностьюal spaces. To prove the regularity of reproducing kernels up to the boundary of 𝒟, we specify them as resolution operators of abstract Neumann problems. The matter thus reduces to a regularity theorem for the Neumann problem, a well-known example being the ??-Neumann problem. The duality itself takes place only for those domains 𝒟 which possess certain convexity properties with respect to A. © 2003 Hindawi Publishing Corporation. All rights reserved.

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Журнал: International Journal of Mathematics and Mathematical Sciences

Выпуск журнала: Vol. 2003, Is. 6

Номера страниц: 327-395


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