On the surjectivity of linear transformations (Q1914779)
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scientific article; zbMATH DE number 894087
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the surjectivity of linear transformations |
scientific article; zbMATH DE number 894087 |
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On the surjectivity of linear transformations (English)
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4 December 1996
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Summary: Let \(B\) be a reflexive Banach space, \(X\) a locally convex space and \(T: B\to X\) (not necessarily bounded) linear transformation. A necessary and sufficient condition is obtained so that for a given \(v\in X\) there is a solution for the equation \(Tu= v\). This result is used to discuss the existence of an \(L^p\)-weak solution of \(Du= v\), where \(D\) is a differential operator with smooth coefficients and \(v\in L^p\).
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admissible linear operators
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harmonic functions
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reflexive Banach space
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locally convex space
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linear transformation
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\(L^ p\)-weak solution
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differential operator
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smooth coefficients
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