Multipliers for continuous frames in Hilbert spaces

Abstract

In this paper we examine the general theory of continuous frame multipliers\nin Hilbert space. These operators are a generalization of the widely used\nnotion of (discrete) frame multipliers. Well-known examples include Anti-Wick\noperators, STFT multipliers or Calder\\'on- Toeplitz operators. Due to the\npossible peculiarities of the underlying measure spaces, continuous frames do\nnot behave quite as well as their discrete counterparts. Nonetheless, many\nresults similar to the discrete case are proven for continuous frame\nmultipliers as well, for instance compactness and Schatten class properties.\nFurthermore, the concepts of controlled and weighted frames are transferred to\nthe continuous setting.\n