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<p>In this research, we explore the gyrator transform (GT) within specific Gelfand-Shilov spaces of type <i>S</i>. We define the continuous gyrator wavelet transform (CGWT) and examine its mapping characteristics in these Gelfand-Shilov spaces. We introduce the CGWT for generalized functions. This paper further discusses the continuity properties of both the GT and CGWT in ultra-differentiable function spaces. Furthermore, we analyze the CGWT of Gevrey functions with compact support.</p>

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Gelfand-Shilov boundedness of the gyrator wavelet transform

  • 期刊论文

  • 发表日期：

    2025年7月10日

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  • Vibha Kumari Sharma,
  • Kanailal Mahato

摘要

In this research, we explore the gyrator transform (GT) within specific Gelfand-Shilov spaces of type S. We define the continuous gyrator wavelet transform (CGWT) and examine its mapping characteristics in these Gelfand-Shilov spaces. We introduce the CGWT for generalized functions. This paper further discusses the continuity properties of both the GT and CGWT in ultra-differentiable function spaces. Furthermore, we analyze the CGWT of Gevrey functions with compact support.