It was mentioned in class that we can take the norm of a function on intervals other than [0,1]. Does it mean that when we talk about the norm of a function, we should first specify the interval we are interested in? And if we don't specify the interval, we take interval [0, 1] as default?
motoole2
When we talk about the norm of a function, we should specify the definition of that norm (not just its interval). There's nothing special with the unit interval [0,1]; it can just as easily be an interval [a,b]. By default, it's probably best to assume that the L2 norm of a function is defined over the space that the function f(x) is defined over.
qhy
So the example above is just part of the L2 norm of the function, right?
motoole2
It depends on the context. If the function f(x) is defined only over the interval [0,1], then it is the L2 norm of that function. If the function f(x) is defined over, say, [-infty,infty], then the integral in the slide is computing the L2 norm of just a part of that function.
It was mentioned in class that we can take the norm of a function on intervals other than [0,1]. Does it mean that when we talk about the norm of a function, we should first specify the interval we are interested in? And if we don't specify the interval, we take interval [0, 1] as default?
When we talk about the norm of a function, we should specify the definition of that norm (not just its interval). There's nothing special with the unit interval
[0,1]; it can just as easily be an interval[a,b]. By default, it's probably best to assume that the L2 norm of a function is defined over the space that the functionf(x)is defined over.So the example above is just part of the L2 norm of the function, right?
It depends on the context. If the function
f(x)is defined only over the interval[0,1], then it is the L2 norm of that function. If the functionf(x)is defined over, say,[-infty,infty], then the integral in the slide is computing the L2 norm of just a part of that function.