Analyticity for some operator functions from statistical quantum mechanics (Q633860)

In statistical quantum mechanics, one considers the particle density \(N\) as a function \(N(V)\) of the real valued potential \(V\). It is shown that, under broad conditions, \(N(V)\) is an analytic function of \(V\). The proof uses the properties of functions which maps the space of square integrable functions onto the space of essentially bounded functions.