SYMMETRICAL HANKEL-OPERATORS - MINIMAL NORM EXTENSIONS AND EIGENSTRUCTURES

The minimal norm extension problem for real partial Hankel matrices is studied: Let x(i), i is-an-element-of alpha subset-or-equal-to n (= ( 1, ..., n)) be given real numbers. Find x(i), i is-an-element-of n \ a lpha, such that the (finite) Hankel matrix [GRAPHICS] has lowest possi ble norm (as an operator on the Euclidean space R(n)). This min-max pr oblem is reduced to an unconstrained maximization problem. It is close to a nonlinear eigenvalue problem. The results suggest a new class of computer algorithms.