An LP analog to AAK theory for p ≥ 2

We develop an L-p analog to AAK theory on the unit circle that interpolates continuously between the case p = infinity, which classically solves for best uniform meromorphic approximation, and the case p = 2, which is equivalent to H-2-best rational approximation. We apply the results to the uniqueness problem in rational approximation and to the asymptotic behaviour of poles of best meromorphic approximants to functions with two branch points. As pointed out by a referee; part of;he theory extends to every p is an element of [1, infinity] when the definition of the Hankel operator is suitably generalized; this we discuss in connection with the recent manuscript by V. A. Prolchorov, submitted for publication. (C) 2002 Elsevier Science (USA).