Duality by reproducing kernels
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 Hilbert structures on subspaces of 𝒮A(𝒟), we show explicit identifications of...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203206037 |
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| Summary: | 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
Hilbert structures on subspaces of 𝒮A(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. |
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| ISSN: | 0161-1712 1687-0425 |