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# An exact inner structure of the block Jacobi-type unitary matrices connected with the corresponding direct and inverse spectral problems

### Abstract

We discuss a problem posed by M. J. Cantero, L. Moral, and L.~Vel\'azquez about representing an arbitrary unitary operator with a CMV-matrix. We consider this problem from the point of view of a one-to-one correspondence between a non-finite unitary operator and an infinite (five-diagonal) block three-diagonal Jacobi-type matrix in the form of the corresponding direct and inverse spectral problems for the trigonometric moment problem. Since the earlier obtained block three-diagonal Jacobi-type unitary matrix has not been fully described, we continue this investigations in the present article. In particular, we show that this exact inner structure coincides with an earlier obtained CMV-matrix.

### Article Information

 Title An exact inner structure of the block Jacobi-type unitary matrices connected with the corresponding direct and inverse spectral problems Source Methods Funct. Anal. Topology, Vol. 14 (2008), no. 2, 168-176 MathSciNet MR2432765 Copyright The Author(s) 2008 (CC BY-SA)

### Authors Information

Mykola E. Dudkin
National Technical University of Ukraine (KPI), 37 Peremogy Prosp., Kyiv, 03056, Ukraine

### Citation Example

Mykola E. Dudkin, An exact inner structure of the block Jacobi-type unitary matrices connected with the corresponding direct and inverse spectral problems, Methods Funct. Anal. Topology 14 (2008), no. 2, 168-176.

### BibTex

@article {MFAT460,
AUTHOR = {Dudkin, Mykola E.},
TITLE = {An exact inner structure of the block Jacobi-type unitary matrices connected with the corresponding direct and inverse spectral problems},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {14},
YEAR = {2008},
NUMBER = {2},
PAGES = {168-176},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=460},
}