Duality by reproducing kernels

A. Shlapunov and N. Tarkhanov

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-69

Abstract:

Let A be a determined or overdetermined elliptic differential operator on a smooth compact manifold X . Write 𝒮 A ( 𝒟 ) for the space of solutions of the system A u = 0 in a domain 𝒟 ⋐ X . Using reproducing kernels related to various Hilbert structures on subspaces of 𝒮 A ( 𝒟 ) , we show explicit identifications of the dual 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 .

Date: 2003
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/IJMMS/2003/387058.pdf (application/pdf)
http://downloads.hindawi.com/journals/IJMMS/2003/387058.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:387058

DOI: 10.1155/S0161171203206037

Access Statistics for this article

More articles in International Journal of Mathematics and Mathematical Sciences from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().