Kernel Thesis Reproduction and Truncated Toeplitz Operators  

作　　者：Zakieldeen Aboabuda Mohamed Alhassn Ali Amna Mahmoud Ahmed Bakhit Isra Abdalhleem Hassan Ali Manal Yagoub Ahmed Juma Tahani Mahmoud Ahmed Mohamed Sumia Izzeldeen Abdallah Abdelmajeed Zakieldeen Aboabuda Mohamed Alhassn Ali;Amna Mahmoud Ahmed Bakhit;Isra Abdalhleem Hassan Ali;Manal Yagoub Ahmed Juma;Tahani Mahmoud Ahmed Mohamed;Sumia Izzeldeen Abdallah Abdelmajeed(Deanship of the Preparatory Year, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia;Department of Mathematic, Faculty of Science, University of Qassim, Buraidah, Saudi Arabia;Department of Mathematic, Gezira Collage of Technology, Khartoum, Sudan)

机构地区：[1]Deanship of the Preparatory Year, Prince Sattam Bin Abdulaziz University, Alkharj, Saudi Arabia [2]Department of Mathematic, Faculty of Science, University of Qassim, Buraidah, Saudi Arabia [3]Department of Mathematic, Gezira Collage of Technology, Khartoum, Sudan

出　　处：《Journal of Applied Mathematics and Physics》2023年第12期4016-4026,共11页应用数学与应用物理（英文）

摘　　要：Important operator characteristics (such boundedness or compactness) for particular classes of operators on particular reproducing kernel Hilbert spaces may be impacted by the behaviour of the operators on the reproducing kernels. These results have been shown for Toeplitz operators on the Paley-Wiener space, a reproducing kernel Hilbert space over C. Furthermore, we show how the norm of such an operator has no relation to the supremum of the norms of the pictures of the normalization reproducing kernels of the space. As a result, if this supremum is finite, the operator is implicitly bounded. To further demonstrate that the operator norm is not the same as the supremum of the norms of the pictures of the real normalized reproducing kernels, another example is also provided. We also set out a necessary and sufficient condition for the operators’ compactness in terms of their limiting function on the reproducing kernels.Important operator characteristics (such boundedness or compactness) for particular classes of operators on particular reproducing kernel Hilbert spaces may be impacted by the behaviour of the operators on the reproducing kernels. These results have been shown for Toeplitz operators on the Paley-Wiener space, a reproducing kernel Hilbert space over C. Furthermore, we show how the norm of such an operator has no relation to the supremum of the norms of the pictures of the normalization reproducing kernels of the space. As a result, if this supremum is finite, the operator is implicitly bounded. To further demonstrate that the operator norm is not the same as the supremum of the norms of the pictures of the real normalized reproducing kernels, another example is also provided. We also set out a necessary and sufficient condition for the operators’ compactness in terms of their limiting function on the reproducing kernels.

关 键 词：Toeplitz Operators Compact Operator The Reproducing Kernel 

分 类 号：O17[理学—数学]