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The Hilbert Sequence And Its Associated Jacobi Matrix, Caleb Beckler
The Hilbert Sequence And Its Associated Jacobi Matrix, Caleb Beckler
Honors Theses
In this project, we investigate positive definite sequences and their associated Jacobi matrices in Hilbert space. We set out to determine the Jacobi matrix associated to the Hilbert sequence by methods described in Akhiezer’s book The Classical Moment Problem. Using methods in Teschl’s book Jacobi Operators and Completely Integrable Nonlinear Lattice, we determine the essential spectrum of the corresponding Jacobi matrix.