Contents
Chapter 1. Introduction 1
Chapter 2. The Toda Hierarchy, Recursion Relations, and Hyperelliptic
Curves 7
Chapter 3. The Stationary Baker-Akhiezer Function 14
Chapter 4. Spectral Theory for Finite-Gap Jacobi Operators 23
Chapter 5. Quasi-Periodic Finite-Gap Solutions of the Stationary Toda
Hierarchy 28
Chapter 6. Quasi-Periodic Finite-Gap Solutions of the Toda Hierarchy and
the Time-Dependent Baker-Akhiezer Function 32
Chapter 7. The Kac-van Moerbeke Hierarchy and its Relation to the Toda
Hierarchy 41
Chapter 8. Spectral Theory for Finite-Gap Dirac-Type Difference Operators 47
Chapter 9. Quasi-Periodic Finite-Gap Solutions of the
Kac-van Moerbeke Hierarchy 50
Appendix A. Hyperelliptic Curves of the Toda-Type and Theta Functions 58
Appendix B. Periodic Jacobi Operators 64
Appendix C. Examples, g = 0,1 71
Acknowledgments 75
Bibliography 76
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