On 2D Inverse Problems/Notation

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

$\mathbb{Z} \mbox{ is the set of integers}$

$\mathbb{R} \mbox{ is the set of real numbers}$

$\mathbb{C} \mbox{ is the set of complex numbers}$

$k, l, m, \dots \mbox{ are integers}$

$a,b,\ldots, \alpha, \beta, \ldots \mbox{ are real and complex numbers and functions}$

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

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

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

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

$\nabla \mbox{ is the gradient}$

$\Delta \mbox{ is the Laplace operator}$

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

$P, Q \mbox{ are ordered subsets of integers}$

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

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

$W(G) \mbox{ is a matrix of exiting probabilities}$

$D_x \mbox{ is a diagonal matrix such that } D_x 1 = x$

$D_A \mbox{ is a diagonal matrix coinciding on diagonal w/matrix } A$

$\lambda \mbox{ is an eigenvalue}$

$\sigma(A) \mbox{ is the spectrum of matrix } A$

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

$P \mbox{ is a permutation matrix}$

$C(A) \mbox{ is a compound matrix of matrix } A$

$F \mbox{ is the Fourier transform}$

$H \mbox{ is the Hilbert transform}$

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

$\Omega \mbox{ is a continuous domain}$

$H^k(\Omega) \mbox{ is a weighted space}$

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

$V \mbox{ is the set of vertices of a graph}$

$E \mbox{ is the set of edges of a graph}$

$w \mbox{ is weight function}$

$M(G) \mbox{ is the medial graph of graph ''G''}$

$\gamma \mbox{ is a conductivity function}$

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

$q \mbox{ is a potential function}$