# On 2D Inverse Problems/Notation

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- $\mathbb {N} {\mbox{ is the set of natural numbers}}$

- $\mathbb {D} =\{z\in \mathbb {C} ,|z|<1\}{\mbox{ is the open unit disc}}$

- $\mathbb {C} ^{+}=\{z\in \mathbb {C} ,\Re (z)\geq 0\}{\mbox{ is the complex right half-plane}}$

- $\omega {\mbox{ is a root of unity}}$

- $M{\mbox{ is a surface (2D manifold)}}$

- $\nabla {\mbox{ is the gradient}}$

- $\Delta =\nabla \cdot \nabla {\mbox{ is the Laplace operator}}$

- $\Lambda {\mbox{ is Dirichlet-to-Neumann operator}}$

- $P,Q{\mbox{ are ordered sets of natural numbers}}$

- $A,B,\ldots {\mbox{ are matrices}}$

- $A(P,Q){\mbox{ is a submatrix of matrix }}A$

- $D_{x}{\mbox{ is a diagonal matrix w/the vector }}x{\mbox{ on the diagonal }}(D_{x}1=x)$

- $D_{A}{\mbox{ is the diagonal matrix, coinciding on diagonal w/the matrix }}A$

- $y,\lambda {\mbox{ is eigenvalue of operator/matrix}}$

- $\sigma (A){\mbox{ is spectrum of matrix }}A,{\mbox{ zeros of characteristic polynomial }}$

- $\rho (A){\mbox{ is the characteristic polynomial of matrix }}A$

- $F_{\omega }{\mbox{ is the Fourier transform}}$

- $H_{\Omega }{\mbox{ is the Hilbert transform}}$

- $\tau {\mbox{ is the Cayley transform}}$

- $\Omega {\mbox{ is a continuous 2Domain}}$

- $G/G^{*}{\mbox{ is graph or network and its dual}}$

- $V_{G}{\mbox{ is the set of vertices of a graph}}$

- $E_{G}{\mbox{ is the set of edges of a graph}}$

- $M_{G}{\mbox{ is the medial graph of an embedded graph }}G$

- $\gamma {\mbox{ is conductivity}}$

- $u,v{\mbox{ are harmonic functions}}$

- $q{\mbox{ is potential function}}$