Expansions in generalized eigenfunctions of selfadjoint operators (Q1113068)
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scientific article; zbMATH DE number 4080219
| Language | Label | Description | Also known as |
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| English | Expansions in generalized eigenfunctions of selfadjoint operators |
scientific article; zbMATH DE number 4080219 |
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Expansions in generalized eigenfunctions of selfadjoint operators (English)
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1989
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A short proof of the existence of an expansion in generalized eigenfunctions of selfadjoint operators in Hilbert spaces is given. Using the existence of an ordered spectral representation the generalized eigenfunctions are given as kernels of suitable Hilbert-Schmidt operators, which in special cases may be constructed from the resolvent and the spectral representation. A result on the regularity of the generalized eigenfunctions as well as first applications to Schrödinger operators are included.
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expansion in generalized eigenfunctions of selfadjoint operators in Hilbert spaces
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ordered spectral representation
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kernels of suitable Hilbert-Schmidt oprators
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Schrödinger operators
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