Highly Nonlinear Approximations for Sparse Signal Representation
List of Symbols
The following notations and symbols will be used without defining them explicitly:![]() |
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union | |
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intersection | |
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subset of | |
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proper subset of | |
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belong(s) | |
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set of all positive integers | |
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set of all integers | |
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field of all real numbers | |
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field of all complex numbers | |
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field of real or complex numbers | |
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is defined by | |
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imply (implies) | |
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if and only if | |
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maps to |
The Kronecker symbol is given by
![$\displaystyle \delta_{ij}=\begin{cases}1 & \text{if $i=j$}\\
0 & \text{otherwise.}
\end{cases}
$](img24.png)
![$ \chi_S$](img25.png)
![$ S$](img26.png)
![$\displaystyle \chi_S(x)=\begin{cases}1 & \text{if $ x\in S$}\\
0 & \text{otherwise.}
\end{cases}
$](img27.png)
![$ n\in \mathbb{N}$](img28.png)
![$ n!$](img29.png)
![$ n!=n(n-1)\cdots 2\cdot1.$](img30.png)
![$ a \in \mathbb{F}$](img31.png)
![$ \vert a\vert$](img32.png)
![$ a\in \mathbb{R}$](img33.png)
![$\displaystyle \vert a\vert=\begin{cases}a & \text{if $a \ge 0$}\\
-a & \text{if $a < 0$}.
\end{cases}
$](img34.png)
![$ a \in \mathbb{C}$](img35.png)
![$ \overline {a}$](img36.png)
![$ \vert a\vert^2=a \overline {a}.$](img37.png)