The Alternative Approach to the Absolute Continuity of Jacobi Matrices with Monotonic Weights
by
Marcin Moszynski
The Institute of Applied Mathematics and Mechanics, Warsaw University

The aim of the talk is to present an application of the subordination theory (due to Khan and Pearson) to the spectral studies for infinite Jacobi matrices (i. e., for selfadjoint operators in the Hilbert space l² given by tridiagonal matrices) with monotonic or ``near-to-monotonic'' weights. This case was intensively studied mainly by J. Dombrowski and S. L. Clark.

Our main result presented here is the absolute continuity for several classes of Jacobi matrices. The simple proof is based on the subordination theory combined with the detailed analysis of the transfer matrices for the solutions of the formal eigenequation. Some of our results are stronger than those obtained by Dombrowski and Clark. For instance, our results work also for some unbounded diagonals.

These results are contained in the paper The alternative approaches to the absolute continuity of Jacobi matrices with monotonic weights joint with Jan Janas.

Date received: April 12, 2000

Copyright © 2000 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caeo-13.