I am not a mathematics student but somehow have to know about L1 and L2 norms. I am looking for some appropriate sources to learn these things and know they work and what are their differences. I am
Triangle inequality Zero norm iff zero vector We could define a $3$-norm where you sum up all the components cubed and take the cubic root. The infinite norm simply takes the maximum component's absolute value as the norm. The $1$-norm simply works by taking the sum of the absolute value of all components. All these norms fulfill the properties ...
Quadratic form involving Frobenius norm Ask Question Asked 1 month ago Modified 1 month ago
Yes, as indicated by daw, because your discrete Sobolev norm only includes the values of the function evaluated at the discrete mesh points, it is always possible to construct a nonzero function that has a zero discrete Sobolev norm.
Are you sure it holds when there’s no norm? The right hand side of your second “equality” is a scalar.
How are $C^0,C^1$ norms defined? I know $L_p,L_\infty$ norms but are the former defined.
Not exactly, sorry. I already know it is bounded, all is left is to find/estimate the operator norm more closely
What can be said of the $C^ {k,\lambda} (\omega)$ -norm of the composition $f\circ\Psi$? It seems one should employ a generalised Faà di Bruno formula (e.g. the explicit one given here), but that approach seems cumbersome at first sight.
That is the definition of the Dirichlet (semi)norm, taken as an analogue of the corresponding concept from complex/harmonic analysis.