On 2D Inverse Problems/Notation

< On 2D Inverse Problems

\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) \ge 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}