| \(\norm{f}_\infty \coloneqq \sup_{x\in
\dom(f)} \abs{f(x)}\) |
The supremum norm |
| \(\norm{f}_{L^\infty} \coloneqq
\inf\theset{M \geq 0 \st \abs{f(x)} \leq M \text{ for a.e. } x
}\) |
The essential supremum |
| \(f_n \convergesto{n \to \infty }
f\) |
Convergence of a sequence |
| \(f(x) \converges{\abs x \to \infty}\to
0\) |
\(f\) vanishes at infinity |
| \(\displaystyle\int_{\abs{x} \geq N} \abs
f \convergesto{N\to \infty} 0\) |
\(f\) has small tails |
| \(\mathcal{H}\) |
A Hilbert space |
| \(X\) |
A topological or metric space |
| \(\del_x f = \dd{}{x}f =
\dd{f}{x}\) |
The partial derivative of \(f\)
with respect to \(x\) |