TY - JOUR
AU1 - Schmüdgen, Konrad
AB - AN OPERATOR-THEORETIC APPROACH TO A COCYCLE PROBLEM IN THE COMPLEX PLANE KONRAD SCHMUDGEN 1. Introduction and main result In this paper we are concerned with the following problem. Letj\x) be a Lebesgue measurable function on the real line. When does there exist a holomorphic function w(z) on the strip {zeC:0<Imz < 1} such that the boundary values w(x + i) and w(x), xeU, exist a.e. and satisfy the equations \w(x)\ = 1 a.e. on U (1) and w(x + i) = w(x)f{x) a.e.onUl (2) (The bar in (2) appears in order to have a more convenient formulation of our main result.) Under some growth assumption concerning w(z) (respectively f{x)), this problem is solved by stating necessary and sufficient conditions for the existence of a solution. Further, a uniqueness result is obtained. The purpose of this note is to give an operator-theoretic treatment of the above problem which might be of interest in itself. We essentially work with the unbounded aP self-adjoint operators e , where aelR and P is the momentum operator —i-r on Cist L (U). As a main technical ingredient we shall use the Stone-von Neumann uniqueness theorem for the canonical commutation relations. In order to formulate 
TI - An Operator‐Theoretic Approach to a Cocycle Problem in the Complex Plane
JF - Bulletin of the London Mathematical Society
DO - 10.1112/blms/27.4.341
DA - 1995-07-01
UR - https://www.deepdyve.com/lp/wiley/an-operator-theoretic-approach-to-a-cocycle-problem-in-the-complex-joiN3kGxRU
SP - 341
EP - 346
VL - 27
IS - 4
DP - DeepDyve
ER -