Havin, V.P. and Nikolski, N.K. (2000) Stanislav Aleksandrovich Vinogradov, His Life and Mathematics. In: Havin, V.P., Nikolski, N.K., Eds., Complex Analysis, Operators, and Related Topics. Operator Theory: Advances and Applications, Birkhäuser, Basel.
https://doi.org/10.1007/978-3-0348-8378-8_1

has been cited by the following article:

• TITLE: Kernel Thesis Reproduction and Truncated Toeplitz Operators

  AUTHORS: 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

  KEYWORDS: Toeplitz Operators, Compact Operator, The Reproducing Kernel

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.12, December 27, 2023

  ABSTRACT: 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.