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• W2097777461 abstract "Let<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$A$ id=E1><mml:mi>A</mml:mi></mml:math>be a determined or overdetermined elliptic differential operator on a smooth compact manifold<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$X$ id=E2><mml:mi>X</mml:mi></mml:math>. Write<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=${mathcal S}_{A}(mathcal{D})$ id=E3><mml:mrow><mml:msub><mml:mi>𝒮</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>𝒟</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>for the space of solutions of the system<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$Au = 0$ id=E4><mml:mrow><mml:mi>A</mml:mi><mml:mi>u</mml:mi><mml:mo>=</mml:mo><mml:mn>0</mml:mn></mml:mrow></mml:math>in a domain<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=${mathcal D}Subset X$ id=E5><mml:mrow><mml:mi>𝒟</mml:mi><mml:mo>⋐</mml:mo><mml:mi>X</mml:mi></mml:mrow></mml:math>. Using reproducing kernels related to various Hilbert structures on subspaces of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=${mathcal S}_{A}(mathcal{D})$ id=E6><mml:mrow><mml:msub><mml:mi>𝒮</mml:mi><mml:mi>A</mml:mi></mml:msub><mml:mrow><mml:mo>(</mml:mo><mml:mi>𝒟</mml:mi><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>, we show explicit identifications of the dual spaces. To prove the regularity of reproducing kernels up to the boundary of<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$mathcal{D}$ id=E7><mml:mi>𝒟</mml:mi></mml:math>, 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<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$bar{partial}$ id=E8><mml:mover accent=true><mml:mo>∂</mml:mo><mml:mo>¯</mml:mo></mml:mover></mml:math>-Neumann problem. The duality itself takes place only for those domains<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$mathcal{D}$ id=E9><mml:mi>𝒟</mml:mi></mml:math>which possess certain convexity properties with respect to<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$A$ id=E10><mml:mi>A</mml:mi></mml:math>." @default.
• W2097777461 created "2016-06-24" @default.
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• W2097777461 date "2003-01-01" @default.
• W2097777461 modified "2023-09-26" @default.
• W2097777461 title "Duality by reproducing kernels" @default.
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• W2097777461 doi "https://doi.org/10.1155/s0161171203206037" @default.
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