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Quantitative spectral stability and sharp Fourier estimates for periodic CMV matrices with decaying perturbations

  • Moacir Aloisio
  • César R. de Oliveira
  • Mariane Pigossi
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Abstract

We study half-line CMV matrices whose Verblunsky coefficients are decaying perturbations of periodic sequences. We quantify the stability of fine properties of the absolutely continuous spectral measure under such perturbations. More precisely, we establish Hölder continuity of the perturbed spectral measure and derive sharp time-averaged Fourier estimates governing the associated quantum dynamics. These results remain valid up to the edges of the absolutely continuous spectrum. Since the spectral measure of a half-line CMV matrix is precisely the orthogonality measure for the corresponding orthogonal polynomials on the unit circle (OPUC), our results also yield new statements for OPUC whose Verblunsky coefficients are decaying perturbations of periodic sequences.

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Cite

BibTeXRIS
BibTeX
@misc{aloisio2026quantitative,
  title = {{Quantitative spectral stability and sharp Fourier estimates for periodic CMV matrices with decaying perturbations}},
  author = {Moacir Aloisio and César R. de Oliveira and Mariane Pigossi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.12856},
  eprint = {2610.12856},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.12856},
}
RIS
TY  - UNPB
TI  - Quantitative spectral stability and sharp Fourier estimates for periodic CMV matrices with decaying perturbations
AU  - Moacir Aloisio
AU  - César R. de Oliveira
AU  - Mariane Pigossi
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2610.12856
UR  - https://arxiv.org/abs/2610.12856
AB  - We study half-line CMV matrices whose Verblunsky coefficients are decaying perturbations of periodic sequences. We quantify the stability of fine properties of the absolutely continuous spectral measure under such perturbations. More precisely, we establish Hölder continuity of the perturbed spectral measure and derive sharp time-averaged Fourier estimates governing the associated quantum dynamics. These results remain valid up to the edges of the absolutely continuous spectrum. Since the spectral measure of a half-line CMV matrix is precisely the orthogonality measure for the corresponding orthogonal polynomials on the unit circle (OPUC), our results also yield new statements for OPUC whose Verblunsky coefficients are decaying perturbations of periodic sequences.
ER  -