Finding all systems of weight functions associated with a given extended Chebyshev space

Systems of weight functions and corresponding generalised derivatives are classically used to build extended Chebyshev spaces on a given interval. This is a well-known procedure. Conversely, if the interval is closed and bounded, it is known that a given extended Chebyshev space can always be associated with a system of weight functions via the latter procedure. In the present article we determine all such possibilities, that is, all systems of weight functions which can be used to define a given extended Chebyshev space on a closed bounded interval.