Journal of Operator Theory

Volume 43, Issue 1, Winter 2000 pp. 171-198.

The method of limit operators for one-dimensional singular integrals with slowly oscillating data

Authors: A. Bottcher (1), Yu.I. Karlovich (2), and V.S. Rabinovich (3)
Author institution: (1) TU Chemnitz, Fakultat fur Mathematik, 09107 Chemnitz, Germany
(2) Instituto Superior Tecnico, Departamento de Matematica, Av. Rovisco Pais, 1096 Lisboa Codex, Portugal
(3) Rostov-on-Don State University, Faculty of Mechanics and Mathematics, Bolshaya Sadovaya Street 105, 344 711 Rostov-on-Don, Russia

Summary: One of the great challenges of the spectral theory of singular integral operators is a theory unifying the three ``forces'' which determine the local spectra: the oscillation of the Carleson curve, the oscillation of the Muckenhoupt weight, and the oscillation of the coefficients. In this paper we demonstrate how by employing the method of limit operators one can describe the spectra in case all data of the operator (the curve, the weight, and the coefficients) are slowly oscillating.

Keywords: Singular integral, Toeplitz operator, pseudodifferential operator, slow oscillation

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