کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5772250 1413354 2017 35 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Kernels of Toeplitz operators on the Hardy space over the bidisk
ترجمه فارسی عنوان
هسته اپراتورهای تئپلیتز در فضای هاردی بیش از بیدز
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
چکیده انگلیسی
We study the kernels of Toeplitz operators on the Hardy space on the bidisk. We first give a sufficient condition for a general symbol to be antiholomorphic under the assumption that the kernel of the corresponding Toeplitz operator contains a backward shift invariant subspace. As an application, we construct an invariant subspace whose its orthogonal complement can not be the kernel of any Toeplitz operator. Also, we give a characterization on a Toeplitz operator for which the orthogonal complement of its kernel is generated by certain inner functions. Finally, we describe all backward shift invariant subspaces which are in the kernels of Toeplitz operators with homogeneous type symbols. As an application, we show that there is a Toeplitz operator for which its kernel has dimension of any given integer and the orthogonal complement of the kernel is generated by two functions. Our result shows that there are higher dimensional phenomena.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 272, Issue 9, 1 May 2017, Pages 3869-3903
نویسندگان
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