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<p>In this article, we explore the generalized Bessel multiplier with respect to a measure space <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\Omega ,\mu )\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi mathvariant="normal">Ω</mi> <mo>,</mo> <mi>μ</mi> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> and examine its properties. We also discuss the conditions for the invertibility of these operators and provide a detailed description of their inverses in relation to the dual continuous frames. Furthermore, we introduce the concept of biorthogonality in the context of Bessel mappings. Then, we survey some properties of generalized Bessel multipliers constructed by the biorthogonal mappings.</p>

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Some new perspectives On the Generalized Bessel Multiplier

  • 期刊论文

  • 发表日期：

    2025年11月7日

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  • F. Arabyani-Neyshaburi,
  • F. Esmaeelzadeh,
  • R. A. Kamyabi Gol,
  • F. Rashid

摘要

In this article, we explore the generalized Bessel multiplier with respect to a measure space \((\Omega ,\mu )\) ( Ω , μ ) and examine its properties. We also discuss the conditions for the invertibility of these operators and provide a detailed description of their inverses in relation to the dual continuous frames. Furthermore, we introduce the concept of biorthogonality in the context of Bessel mappings. Then, we survey some properties of generalized Bessel multipliers constructed by the biorthogonal mappings.