# Errata for Jacobi Operators andCompletely Integrable Nonlinear Lattices Gerald Teschl

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Page numbers are as found in the published book.

1. p342, Ref. [232]: "pPapers" should read "Papers"
2. p118, Thm 7.3(ii): the square should be removed from $\Delta(z)^2$
3. p116, (7.7): $M(z,n_0)$ should be replaced by $M(z,n_0)^{-1}$
4. p22, (1.136): should read l.h.s. = - r.h.s. = - r.h.s.
5. p25, (1.154): should read l.h.s. = - r.h.s.
6. p147, proof of Lemma 8.15: "(8.81) and (8.81)" should read"(8.78) and (8.81)"
7. p150, (8.108): a factor $4a(n)^2$ is missing on the r.h.s.
8. p158, line after (9.39): a factor $\mathbb{R}$ should read $\mathbb{R}^g$
9. p. 295: lines after (A.122): $E_{\ell-1}$ should read $E_{2\ell-1}$ and$E_{\ell}$ should read $E_{2\ell}$
10. p285, line after (A.79): "picture on page 2" should read "picture on page 275"
11. p248, first line: "cart" should read "chart"
12. p158, paragraph after (9.41) : replace $E_1, E_2, E_3$ by $E_0, E_1, E_2$, respectively
13. p131, lines before (7.114): replace "(2.124)" by "(2.131)"
14. p131, (7.114): $U_i(\lambda,m)$ should read $\overline{U_i(\lambda,m)}$. Similarly inthe following line and in (7.115)
15. p71, (3.85): The square around the sum is missing
16. p128, Thm 7.11: In the last statement $H_p$ should be replaced by $H$
17. p47, (2.153): a factor $1/\pi$ is missing on the r.h.s.
18. p127, (7.86): $\lim_{n\to \infty}$ should read $\lim_{n\to \pm\infty}$
19. p127, (7.87): the sign in front of the sum must be switched from $\mp$ to $\pm$
20. p183, (10.116): $k_\ell^{....+\ell}$ must be changed to $k_\ell^{....+j}$ in both lines
21. p183, (10.117): the upper limit $\infty$ in the first sum is missing
22. p171, (10.32): The sign of the sum must be changed.
23. p172, second line: $f_\pm(k,n) = k^{\mp n} (....)$ should read $f_\pm(k,n) = k^{\pm n} (....)$
24. p172, (10.33): the constant terms $\frac{1}{2}\alpha(k)$ respectively $\frac{1}{2 k^2}\alpha(k)$must be switched. Moreover it should read $m\to-\infty$ in the first line and $n\to+\infty$ in the secondline.
25. p172, (10.34): The sign of the sum must be changed.
26. p174, line after (10.50): |W(...)|/2 should read 2|W(...)|
27. p58, Thm 3.2: the last sentence should read "The spectrum of $H_+$ is simple."
28. p185, (11.1): there is a minus missing on the r.h.s (both times)
29. p185, (11.23): there is a minus missing on the r.h.s
30. p99, first line after the proof of Lemma 5.18: the second Weyl $m$-function should havea minus sign instead of a plus sign in the subscript
31. p118, (7.29) should read $\phi_\pm(z,n)=$ and not $\phi_\pm(z,n_0)=$
32. p250, (13.72): in the formula for $R_\pm$ there is a 2 missing in the exponential
33. p251, (13.76): the norm should be squared
34. p179, Thm 10.10: the proof for the claim that $\mathcal{F}$ is trace class is wrong
35. p293, Lem A.6: the definition of $\tilde{D}$ must be changed if $p$ is a branch point:$\tilde{D}(p)= \lfloor\frac{D(p)+1}{2}\rfloor$
36. p267, Thm 14.13: the TL after (14.86) should read TLr. Similarly in Thm 14.14after (14.88)
37. p264, (14.66)-(14.68): $\tau_{+\infty,-\infty}$ should be $\omega_{\infty_+,\infty_-}$
38. p194, (11.59)-(11.61),(11.66): $\tau_{\infty_+,\infty_-}$ should be $\omega_{\infty_+,\infty_-}$
39. p195, line after (11.67): $2[...] \in J(M)$ should read $2[...] = [0]$
40. p252, line after (13.83): the reference (7.30) should point to (6.26)
41. p254, (13.99): the plus signs inside sn(...) should be a minus sign
42. p159, (9.43): it should be $\tilde{a}^{-1}=...$
43. p247, (13.51): $\tilde{f}_{s-\ell}(n,t)$ should read $\tilde{g}_{s-\ell}(n,t)$
44. p175, (10.61): $\cos(m \mathrm{E}^{\mathrm{i} \varphi}$ should read $\cos(m \varphi)$
45. p254, (13.96): $(E_1-E_3)$ should read $(E_3-E_1)$