کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4591863 1335058 2008 18 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Homogeneous operators on Hilbert spaces of holomorphic functions
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Homogeneous operators on Hilbert spaces of holomorphic functions
چکیده انگلیسی

In this paper we construct a large class of multiplication operators on reproducing kernel Hilbert spaces which are homogeneous with respect to the action of the Möbius group consisting of bi-holomorphic automorphisms of the unit disc D. Indeed, this class consists of exactly those operators for which the associated unitary representation of the universal covering group of the Möbius group is multiplicity free. For every m∈N we have a family of operators depending on m+1 positive real parameters. The kernel function is calculated explicitly. It is proved that each of these operators is bounded, lies in the Cowen–Douglas class of D and is irreducible. These operators are shown to be mutually pairwise unitarily inequivalent.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 254, Issue 9, 1 May 2008, Pages 2419-2436