I was wondering how I can show that any linear map $T: L^1(\Omega) \rightarrow L^{\infty}(\Omega)$ can be represented as an integral operator
$$T(f)(x):=\int_{\Omega} K(x,y)f(y) dy.$$
Does anybody know how to show this or where this follows from?
I was wondering how I can show that any linear map $T: L^1(\Omega) \rightarrow L^{\infty}(\Omega)$ can be represented as an integral operator
$$T(f)(x):=\int_{\Omega} K(x,y)f(y) dy.$$
Does anybody know how to show this or where this follows from?
Copyright © 2021 JogjaFile Inc.
Here you will find your theorem, a sketch of its proof, some historical remarks and a generalisation.