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<p>We characterize the compact aggregate Toeplitz operators on the spaces of all entire functions and all real analytic functions in the real line. Motivated by our previous research concerning the space of all real analytic functions, we develop a theory of integral kernel operators on the spaces of all entire functions. In both cases we characterize the compact integral kernel operators. Finally, we prove that every compact operator is of symbol zero in both cases.</p>

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Compactness of the Aggregate Toeplitz Operators and the General Integral Kernel Operators in the Case of all Entire Functions and all Real Analytic Functions on the Real Line

  • 期刊论文

  • 发表日期：

    2026年3月6日

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  • Michał Jasiczak

摘要

We characterize the compact aggregate Toeplitz operators on the spaces of all entire functions and all real analytic functions in the real line. Motivated by our previous research concerning the space of all real analytic functions, we develop a theory of integral kernel operators on the spaces of all entire functions. In both cases we characterize the compact integral kernel operators. Finally, we prove that every compact operator is of symbol zero in both cases.