Asymptotic expansion of the eigenvalues of a Toeplitz matrix with a real symbol
Abstract
Asymptotic expansion of the eigenvalues of a Toeplitz matrix with real symbol. This work provides two results obtained as a consequence of an inversion formula for Toeplitz matrices with real symbol. First we obtain an symptotic expression for the minimal eigenvalues of a Toeplitz matrix with a symbol which is periodic, even and derivable on $[0, 2\pi[$. Next we prove that a Toeplitz band matrix with a symbol without zeros on the united circle is invertible with an inverse which is essentially a band matrix. As a consequence of this last statement we give an asymptotic estimation for the entries of the inverse of a Toplitz matrix with a regular symbol.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2021
- DOI:
- 10.48550/arXiv.2104.12394
- arXiv:
- arXiv:2104.12394
- Bibcode:
- 2021arXiv210412394R
- Keywords:
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- Mathematics - Classical Analysis and ODEs
- E-Print:
- in French. arXiv admin note: text overlap with arXiv:1512.04296