# Errata for Jacobi Operators andCompletely Integrable Nonlinear Lattices Gerald Teschl

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