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The Factorization a...
The Factorization and Representation of Operators in the Algebra Generated by Toeplitz Operators
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- Kailath, Thomas (författare)
- Stanford University, CA, USA
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- Levy, Bernard (författare)
- Stanford University, CA, USA
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- Ljung, Lennart, 1946- (författare)
- Linköpings universitet,Reglerteknik,Tekniska högskolan
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- Morf, Martin (författare)
- Stanford University, CA, USA
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(creator_code:org_t)
- SIAM, 1979
- 1979
- Engelska.
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Ingår i: SIAM Journal on Applied Mathematics. - : SIAM. - 0036-1399 .- 1095-712X. ; 37:3, s. 467-484
- Relaterad länk:
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Ämnesord
Stäng
- In this paper, we study the factorization and the representation of Fredholm operators belonging to the algebra $\mathcal{R}$ generated by inversion and composition of Toeplitz integral operators. The operators in $\mathcal{R}$ have the interesting property of being close to Toeplitz (in a sense quantifiable by an integer-valued index $\alpha $) and, at the same time, of being dense in the space of arbitrary kernels. By using these properties, we derive a set of efficient algorithms (generalized fast-Cholesky and Levinson recursions) for the factorization and the inversion of arbitrary Fredholm operators. The computational burden of these algorithms depends on how close (as measured by the index $\alpha $) these operators are to being Toeplitz.We also obtain several important representation theorems for the decomposition of operators in $\mathcal{R}$ in terms of sums of products of lower times upper triangular Toeplitz operators. These results can be used to approximate operators corresponding to noncausal and time-variant systems in terms of operators representing causal and anticausal time-invariant systems, a property that has a large number of potential applications in signal processing problems.
Ämnesord
- TEKNIK OCH TEKNOLOGIER -- Elektroteknik och elektronik -- Reglerteknik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Electrical Engineering, Electronic Engineering, Information Engineering -- Control Engineering (hsv//eng)
Nyckelord
- Toeplitz operator
- Fredholm operators
- Factorization
- Representation
Publikations- och innehållstyp
- ref (ämneskategori)
- art (ämneskategori)
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