I have not been able to obtain a clear definition of what is currently called a 'continuous matrix' nor 'continuous matrix operators.'
It is unclear if the definition would involve a matrix with continuous elements such as continuous functions, or if somehow the matrix itself is to be considered continuous. In the latter case, I would imagine an example of a continuous matrix to be the Green's Function for a function, where integration of a function by its Green's function would be akin to some sort of continuous matrix multiplication.
So I would like to ask:
What is the current accepted definition for a continuous matrix and a continuous matrix operator?
Is there an existing definition for a continuous matrix, of the type I mention, where Green's Function is an example of such a matrix?
If there is such a definition (2.) then does someone know of a clear reference for the theory? I would appreciate both pure and applied works.