The aim of this paper is to introduce a class of B-splines <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1688_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">${\phi }_n$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϕ</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> on the Heisenberg group <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1688_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {H}}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">H</mi> </math></EquationSource> </InlineEquation> and prove certain fundamental properties. The non-commutative group structure of <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1688_Article_IEq2.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="13" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {H}}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">H</mi> </math></EquationSource> </InlineEquation> leads to very different results for <InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1688_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">${\phi }_n$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi>ϕ</mi> <mi>n</mi> </msub> </math></EquationSource> </InlineEquation> from those of the classical B-splines on the real line <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="11785_2025_1688_Article_IEq5.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="12" /> </InlineMediaObject> <EquationSource Format="TEX">${\mathbb {R}}$</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">R</mi> </math></EquationSource> </InlineEquation>.

B-splines on the Heisenberg Group

期刊论文
出版模式：

开放获取
发表日期：

2025年4月23日

查看全文

S. R. Das,
P. Massopust,
R. Radha

摘要

The aim of this paper is to introduce a class of B-splines ${\phi }_n$ $ϕ_{n}$ on the Heisenberg group ${\mathbb {H}}$ $H$ and prove certain fundamental properties. The non-commutative group structure of ${\mathbb {H}}$ $H$ leads to very different results for ${\phi }_n$ $ϕ_{n}$ from those of the classical B-splines on the real line ${\mathbb {R}}$ $R$ .