Scholarlink

<p>In this study, a weighted generalization of the Fourier transform using a weight function <i>w</i> with respect to a function <i>g</i> is defined and some fundamental properties are examined. Then, the existence of the weighted Fourier transform is proven, and the transforms of some example functions are calculated to facilitate understanding of the transform, and then the inverse of the weighted Fourier transform is given. Furthermore, a new weighted convolution operation is defined, and a weighted convolution theorem is proven. Finally, the weighted Fourier transform of the weighted derivative and the fractional weighted derivative of a function <i>f</i> with a weighted <i>w</i> respect to another function <i>g</i> is investigated. Additionally, the certain theorems are verified with examples, and our study is enriched with numerical graphs.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Generalizing the Fourier Transform for Weighted Differential Operators

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年7月20日

查看全文
  • Emre Sermutlu,
  • Fahd Jarad,
  • Serdal Yazıcı,
  • Bayram Çekim

摘要

In this study, a weighted generalization of the Fourier transform using a weight function w with respect to a function g is defined and some fundamental properties are examined. Then, the existence of the weighted Fourier transform is proven, and the transforms of some example functions are calculated to facilitate understanding of the transform, and then the inverse of the weighted Fourier transform is given. Furthermore, a new weighted convolution operation is defined, and a weighted convolution theorem is proven. Finally, the weighted Fourier transform of the weighted derivative and the fractional weighted derivative of a function f with a weighted w respect to another function g is investigated. Additionally, the certain theorems are verified with examples, and our study is enriched with numerical graphs.