DPhil thesis errata

Page 12, line -3: $t^{n+1/2}$ is defined for $n \in \{0, \dotsc, M-1\}$, but it is actually never used.

Page 71, proof of Lemma 3.16: All instances of $\mathrm{H}(\mathsf{D};\mathrm{M})$ and $\mathrm{H}(D_i;M_i)$ must be replaced with $\mathrm{H}^1_{\mathsf{M}}(\mathsf{D})$ and $\mathrm{H}^1_{M_i}(D_i)$, respectively.

Page 91, eq. (3.75): Within the first expression of the equation, $\hat{L}^2(\tau_l - \tau_k) - \hat{L}^2(\tau_k)$ should read $\hat{L}^2(\tau_l) - \hat{L}^2(\tau_k)$.

Page 91, eq. (3.78a): Where it reads $\partial_{\boldsymbol{\alpha}} \in \mathrm{L}^2_{\mathsf{M}}(\mathsf{D})$ it should read $\partial_{\boldsymbol{\alpha}} \varphi \in \mathrm{L}^2_{\mathsf{M}}(\mathsf{D})$.

Page 92, eq. (3.79a): Where it reads $\partial_{\boldsymbol{\alpha}} \in \mathrm{L}^2_{\mathsf{M}}(\mathsf{D})$ it should read $\partial_{\boldsymbol{\alpha}} \varphi \in \mathrm{L}^2_{\mathsf{M}}(\mathsf{D})$.

Page 92, third line of the proof of Lemma 3.29: "Also, by the definitions in (3.39), (3.40) and (3.48)" should read "Also, by the definitions in (3.39) and (3.40)".

Page 94, second equation (with no number): Where it reads $\varphi \ni \mathrm{H}^1_0$ it should read $\varphi \ni \mathrm{H}^1_0(\mathsf{D})$.

Page 138, line 12: Where it reads "from the spectrum of $T$" it should read "from the point spectrum of $T$".