Finite eigenfuction approximations for continuous spectrum operators
In this paper, we introduce a new formulation of the theory of continuous spectrum eigenfunction expansions for self-adjoint operators and analyze the question of when operators may be approximated in an operator norm by finite sums of multiples of eigenprojections of multiplicity one. The theory is...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
1993-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171293000018 |
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| Summary: | In this paper, we introduce a new formulation of the theory of continuous spectrum
eigenfunction expansions for self-adjoint operators and analyze the question of when operators
may be approximated in an operator norm by finite sums of multiples of eigenprojections of
multiplicity one. The theory is designed for application to ordinary and partial differential
equations; relationships between the abstract theory and differential equations are worked out in
the paper. One motivation for the study is the question of whether these expansions are
susceptible to computation on a computer, as is known to be the case for many examples in the
discrete spectrum case. The point of the paper is that continuous and discrete spectrum
eigenfunction expansions are treated by the same formalism; both are limits in an operator norm
of finite sums. |
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| ISSN: | 0161-1712 1687-0425 |