MULTIPLIERS OF HILBERT SPACES OF ANALYTIC FUNCTIONS ON THE COMPLEX HALF-PLANE

作者：Kucik Andrzej Stanislaw^*

来源：Operators and Matrices, 2017, 11(2): 435-453.

DOI：10.7153/oam-11-29

• Banach algebras
• Banach spaces
• Bergman spaces
• Carleson measures
• Dirichlet spaces
• Hardy spaces
• Hardy-Sobolev spaces
• Hilbert spaces
• Laplace transform
• maximal ideal spaces
• multiplication operators
• multipliers
• reproducing kernels
• spaces of analytic functions
• weighted L-2 spaces
• Zen spaces

It follows, from a generalised version of Paley-Wiener theorem, that the Laplace transform is an isometry between certain spaces of weighted L-2 functions defined on (0,infinity) and (Hilbert) spaces of analytic functions on the right complex half-plane (for example Hardy, Bergman or Dirichlet spaces). We can use this fact to investigate properties of multipliers and multiplication operators on the latter type of spaces. In this paper we present a full characterisation of multipliers in terms of a generalised concept of a Carleson measure. Under certain conditions, these spaces of analytic functions are not only Hilbert spaces but also Banach algebras, and are therefore contained within their spaces of multipliers. We provide some necessary as well as sufficient conditions for this to happen and look at its consequences.

• 出版日期2017-6