Some general preliminary considerations
Each function defines a functional in the following way:
Such functional we will call regular functional and function — its generator.
For each , we will consider a functional defined as follows:
Since generally, we can not speak about values at the point for functions from , in the following, we assume some regularity for functions from considered spaces, so that (1) is correctly defined.
Necessary notations and motivation
Definition of Green’s function
If the functional is regular with generator , then is called Green’s function of operator and solution of (2) admits the following integral representation:
|Date of creation||2013-03-22 14:43:36|
|Last modified on||2013-03-22 14:43:36|
|Last modified by||PrimeFan (13766)|