On the structure of the inverse to Toeplitz-block Toeplitz matrices and of the corresponding polynomial reflection coefficients
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- by Alexander Sakhnovich PDF
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Abstract:
The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the 1-D (one-dimensional) case are classical and have numerous applications. We consider the 2-D case of Toeplitz-block Toeplitz matrices, describe a minimal information, which is necessary to recover the inverse matrices, and give a complete characterization of the inverse matrices. A 2-D analogue of the important Ambartsumyan and Sobolev formulas for the corresponding reflection coefficients is derived as well.References
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Additional Information
- Alexander Sakhnovich
- Affiliation: Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, A-1090 Vienna, Austria
- MR Author ID: 310542
- Email: oleksandr.sakhnovych@univie.ac.at
- Received by editor(s): August 11, 2017
- Received by editor(s) in revised form: July 21, 2018, and October 8, 2018
- Published electronically: February 11, 2019
- Additional Notes: The author’s research was supported by the Austrian Science Fund (FWF) under Grant No. P29177.
- © Copyright 2019 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 372 (2019), 5547-5570
- MSC (2010): Primary 15A09, 15B05; Secondary 94A99
- DOI: https://doi.org/10.1090/tran/7770
- MathSciNet review: 4014287