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PACKING SUBORDINACY WITH APPLICATION TO SPECTRAL CONTINUITY

Part of: Classical measure theory Difference and functional equations Difference equations General theory of linear operators

Published online by Cambridge University Press:  13 June 2019

V. R. BAZAO ,
S. L. CARVALHO  and
C. R. DE OLIVEIRA
V. R. BAZAO
Affiliation:
Faculdade de Ciências Exatas e Tecnologias, UFGD Dourados, MS, 79804-970, Brazil
S. L. CARVALHO
Affiliation:
Departamento de Matemática, UFMG, Belo Horizonte, MG, 30161-970, Brazil
C. R. DE OLIVEIRA*
Affiliation:
Departamento de Matemática, UFSCar, São Carlos, SP, 13560-970, Brazil email oliveira@dm.ufscar.br
*
✉oliveira@dm.ufscar.br
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Abstract

By using methods of subordinacy theory, we study packing continuity properties of spectral measures of discrete one-dimensional Schrödinger operators acting on the whole line. Then we apply these methods to Sturmian operators with rotation numbers of quasibounded density to show that they have purely $\unicode[STIX]{x1D6FC}$-packing continuous spectrum. A dimensional stability result is also mentioned.

Keywords

subordinacy theorypacking measuresSturmian potentialsspectral theory

MSC classification

Primary: 47A10: Spectrum, resolvent
Secondary: 39A70: Difference operators 28A78: Hausdorff and packing measures
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 108 , Issue 2 , April 2020 , pp. 226 - 244
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

V.R.B. thanks CAPES for financial support. S.L.C. thanks the partial support by FAPEMIG (Universal Project CEX-APQ-00554-13). CRdO thanks the partial support by CNPq (Universal Project 41004/2014-8).

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