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<p>We present in this paper constructions of orthogonal multiresolution analyses on a compact Riemannian manifold <i>V</i> of dimension <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13226_2025_866_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="79" /> </InlineMediaObject> <EquationSource Format="TEX">\(n~(n\in \mathbb {N}^*)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>n</mi> <mspace width="3.33333pt" /> <mo stretchy="false">(</mo> <mi>n</mi> <mo>∈</mo> <msup> <mrow> <mi mathvariant="double-struck">N</mi> </mrow> <mo>∗</mo> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation> by using the solution of minimization problem. The associated wavelet bases are generated by a finite number of basic functions called splines and have location properties. To realize this object, we prove at first some lemmas of algebra and functional analysis, then we characterize some functional spaces with new norms.</p>

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Wavelets on a Riemannian compact manifold

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Hatem Bibi

摘要

We present in this paper constructions of orthogonal multiresolution analyses on a compact Riemannian manifold V of dimension \(n~(n\in \mathbb {N}^*)\) n ( n ∈ N ∗ ) by using the solution of minimization problem. The associated wavelet bases are generated by a finite number of basic functions called splines and have location properties. To realize this object, we prove at first some lemmas of algebra and functional analysis, then we characterize some functional spaces with new norms.