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<p>This paper aims to contribute to the theory of superoscillations and supershifts. It provides an overview and new insights into the theory. A crucial role in the evolution of superoscillations and supershifts is played by infinite-order differential operators acting on a suitable class of holomorphic functions. In this work, we consider partial differential equations with a convolution term and determine the corresponding expressions for their associated infinite-order operators. We also consider linear partial differential-difference equations, defining the associated infinite-order differential operator in this case.</p>

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Some Infinite Order Differential Operators Associated with Superoscillations in Several variables

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年3月3日

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  • Fabrizio Colombo,
  • Elodie Pozzi,
  • Irene Sabadini,
  • Brett D. Wick

摘要

This paper aims to contribute to the theory of superoscillations and supershifts. It provides an overview and new insights into the theory. A crucial role in the evolution of superoscillations and supershifts is played by infinite-order differential operators acting on a suitable class of holomorphic functions. In this work, we consider partial differential equations with a convolution term and determine the corresponding expressions for their associated infinite-order operators. We also consider linear partial differential-difference equations, defining the associated infinite-order differential operator in this case.