Asymptotic behaviour of a dynamic local field: is the order of the k to infinity and omega to infinity limits interchangeable in an interacting many-body system?

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Abstract
The wavevector- and frequency-dependent susceptibility chi k( omega ) in many-body theory is customarily expressed in terms of a dynamic local field term Gk( omega ). For k to infinity there are certain asymptotic forms for Gk( omega ) due to Shaw (1970) and to Niklasson (1974). It is shown that they represent the two different orders of the k to infinity and omega to infinity limits. The validity of the result is tested in an exactly solvable physical system.