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<p>A two-sided Bargmann space is defined to extend the notion of the quaternionic Bargmann space of slice regular functions to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1751_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="19" /> </InlineMediaObject> <EquationSource Format="TEX">\({\mathbb {H}}^2 \)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">H</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>. A systematic study is presented and includes a precise description of its middle hilbertian structure, its two-sided orthogonal basis, related reproducing kernel and its integral representation by a two-sided Bargmann type transform.</p>

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The two-sided Bargmann Space

  • 期刊论文

  • 发表日期：

    2025年7月16日

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  • R. Elhoua,
  • A. Ghanmi,
  • A. Maarouf

摘要

A two-sided Bargmann space is defined to extend the notion of the quaternionic Bargmann space of slice regular functions to \({\mathbb {H}}^2 \) H 2 . A systematic study is presented and includes a precise description of its middle hilbertian structure, its two-sided orthogonal basis, related reproducing kernel and its integral representation by a two-sided Bargmann type transform.