## NotationEdit

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

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

- $\mathbb {R} ^{N}{\mbox{ is the N-dimensional Euclidean space}}$

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

- $a,b,\ldots {\mbox{ are real and complex numbers}}$

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

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

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

- $M{\mbox{ is surface}}$

- $\alpha ,\beta ,\ldots {\mbox{ are analytic functions}}$

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

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

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

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

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

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

- $\lambda {\mbox{ is eigenvalue}}$

- $\rho {\mbox{ is characteristic polynomial}}$

- $P{\mbox{ is permutation matrix}}$

- $F{\mbox{ is Fourier transform}}$

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

- $\Gamma /\Gamma ^{*}{\mbox{ is graph and its dual}}$

- $V{\mbox{ is the set of vertices}}$

- $E{\mbox{ is the set of edges}}$

- $w{\mbox{ is weight function}}$

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

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

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

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

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