On 2D Inverse Problems/Notation

< On 2D Inverse Problems

\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 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

\lambda \mbox{ is an eigenvalue of an operator/matrix}

\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 an embedded graph } G

\gamma \mbox{ is a conductivity function}

u, v  \mbox{ are harmonic functions}

q \mbox{ is a potential function}