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DVD206/Notation
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Notation
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N
is the set of integers
{\displaystyle \mathbb {N} {\mbox{ is the set of integers}}}
R
is the set of real numbers
{\displaystyle \mathbb {R} {\mbox{ is the set of real numbers}}}
R
N
is the N-dimensional Euclidean space
{\displaystyle \mathbb {R} ^{N}{\mbox{ is the N-dimensional Euclidean space}}}
C
is the set of complex numbers
{\displaystyle \mathbb {C} {\mbox{ is the set of complex numbers}}}
a
,
b
,
…
are real and complex numbers
{\displaystyle a,b,\ldots {\mbox{ are real and complex numbers}}}
C
+
=
{
z
∈
C
,
ℜ
(
z
)
≥
0
}
is the complex right half-plane
{\displaystyle \mathbb {C} ^{+}=\{z\in \mathbb {C} ,\Re (z)\geq 0\}{\mbox{ is the complex right half-plane}}}
D
=
{
z
∈
C
,
|
z
|
≤
1
}
is the closed unit disc
{\displaystyle \mathbb {D} =\{z\in \mathbb {C} ,|z|\leq 1\}{\mbox{ is the closed unit disc}}}
ω
is root of unity
{\displaystyle \omega {\mbox{ is root of unity}}}
M
is surface
{\displaystyle M{\mbox{ is surface}}}
α
,
β
,
…
are analytic functions
{\displaystyle \alpha ,\beta ,\ldots {\mbox{ are analytic functions}}}
∇
is gradient
{\displaystyle \nabla {\mbox{ is gradient}}}
Δ
is Laplace operator
{\displaystyle \Delta {\mbox{ is Laplace operator}}}
Λ
is Dirichlet-to-Neumann operator
{\displaystyle \Lambda {\mbox{ is Dirichlet-to-Neumann operator}}}
k
,
l
,
m
are integers
{\displaystyle k,l,m{\mbox{ are integers}}}
P
,
Q
are ordered subsets of integers
{\displaystyle P,Q{\mbox{ are ordered subsets of integers}}}
A
,
B
,
…
are matrices
{\displaystyle A,B,\ldots {\mbox{ are matrices}}}
λ
is eigenvalue
{\displaystyle \lambda {\mbox{ is eigenvalue}}}
ρ
is characteristic polynomial
{\displaystyle \rho {\mbox{ is characteristic polynomial}}}
P
is permutation matrix
{\displaystyle P{\mbox{ is permutation matrix}}}
F
is Fourier transform
{\displaystyle F{\mbox{ is Fourier transform}}}
H
k
(
Ω
)
is a weighted space
{\displaystyle H^{k}(\Omega ){\mbox{ is a weighted space}}}
Γ
/
Γ
∗
is graph and its dual
{\displaystyle \Gamma /\Gamma ^{*}{\mbox{ is graph and its dual}}}
V
is the set of vertices
{\displaystyle V{\mbox{ is the set of vertices}}}
E
is the set of edges
{\displaystyle E{\mbox{ is the set of edges}}}
w
is weight function
{\displaystyle w{\mbox{ is weight function}}}
G
/
G
∗
is network and its dual
{\displaystyle G/G^{*}{\mbox{ is network and its dual}}}
M
(
G
)
is the medial graph
{\displaystyle M(G){\mbox{ is the medial graph}}}
γ
is conductivity
{\displaystyle \gamma {\mbox{ is conductivity}}}
u
,
v
are harmonic functions
{\displaystyle u,v{\mbox{ are harmonic functions}}}
q
is potential
{\displaystyle q{\mbox{ is potential}}}
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