Phase retrieval of H2-functions

This paper concerns the problem of determining an H2-function f when |f(x)| is known for almost all x. It is shown that the conditions and together imply that either g=Vf or , where V has period b. Under certain restrictions on f and g the function V takes the form , where B1, and B2, are Blaschke products. If the conditions (*) and (**) hold for three incommensurable b's, then g is constant multiple of f. Analogous results for the problem of magnitude retrieval of H2-functions are discussed briefly.