Small-time asymptotics for subelliptic Hermite functions on $SU(2)$ and the CR sphere
We show that, under a natural scaling, the small-time behavior of the logarithmic derivatives of the subelliptic heat kernel on $SU(2)$ converges to their analogues on the Heisenberg group at time 1. Realizing $SU(2)$ as $\mathbb{S}^3$, we then generalize these results to higher-order odd-dimensiona...
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| creator | Campbell, Joshua Melcher, Tai |
| description | We show that, under a natural scaling, the small-time behavior of the
logarithmic derivatives of the subelliptic heat kernel on $SU(2)$ converges to
their analogues on the Heisenberg group at time 1. Realizing $SU(2)$ as
$\mathbb{S}^3$, we then generalize these results to higher-order
odd-dimensional spheres equipped with their natural subRiemannian structure,
where the limiting spaces are now the higher-dimensional Heisenberg groups. |
| doi_str_mv | 10.48550/arxiv.1710.02550 |
| format | Article |
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logarithmic derivatives of the subelliptic heat kernel on $SU(2)$ converges to
their analogues on the Heisenberg group at time 1. Realizing $SU(2)$ as
$\mathbb{S}^3$, we then generalize these results to higher-order
odd-dimensional spheres equipped with their natural subRiemannian structure,
where the limiting spaces are now the higher-dimensional Heisenberg groups.</description><identifier>DOI: 10.48550/arxiv.1710.02550</identifier><language>eng</language><subject>Mathematics - Analysis of PDEs</subject><creationdate>2017-10</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1710.02550$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1710.02550$$DView paper in arXiv$$Hfree_for_read</backlink><backlink>$$Uhttps://doi.org/10.1007/s11118-019-09798-4$$DView published paper (Access to full text may be restricted)$$Hfree_for_read</backlink></links><search><creatorcontrib>Campbell, Joshua</creatorcontrib><creatorcontrib>Melcher, Tai</creatorcontrib><title>Small-time asymptotics for subelliptic Hermite functions on $SU(2)$ and the CR sphere</title><description>We show that, under a natural scaling, the small-time behavior of the
logarithmic derivatives of the subelliptic heat kernel on $SU(2)$ converges to
their analogues on the Heisenberg group at time 1. Realizing $SU(2)$ as
$\mathbb{S}^3$, we then generalize these results to higher-order
odd-dimensional spheres equipped with their natural subRiemannian structure,
where the limiting spaces are now the higher-dimensional Heisenberg groups.</description><subject>Mathematics - Analysis of PDEs</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNqFzrsOgkAQheFtLIz6AFZOQaEFCCjRnmioRWqy4hAm2Vt2FyNvLxJ7q5N8OcXP2DqJo-M5y-I9t296RclphDgdYc6qUnIhQk8SgbtBGq89NQ5abcH1DxSCzAhQoJXkEdpeNZ60cqAVBGW1TXcBcPUE3yHkN3CmQ4tLNmu5cLj67YJtrpd7XoRTQG0sSW6H-htSTyGH_48P8F49Kw</recordid><startdate>20171006</startdate><enddate>20171006</enddate><creator>Campbell, Joshua</creator><creator>Melcher, Tai</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20171006</creationdate><title>Small-time asymptotics for subelliptic Hermite functions on $SU(2)$ and the CR sphere</title><author>Campbell, Joshua ; Melcher, Tai</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-arxiv_primary_1710_025503</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Mathematics - Analysis of PDEs</topic><toplevel>online_resources</toplevel><creatorcontrib>Campbell, Joshua</creatorcontrib><creatorcontrib>Melcher, Tai</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Campbell, Joshua</au><au>Melcher, Tai</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Small-time asymptotics for subelliptic Hermite functions on $SU(2)$ and the CR sphere</atitle><date>2017-10-06</date><risdate>2017</risdate><abstract>We show that, under a natural scaling, the small-time behavior of the
logarithmic derivatives of the subelliptic heat kernel on $SU(2)$ converges to
their analogues on the Heisenberg group at time 1. Realizing $SU(2)$ as
$\mathbb{S}^3$, we then generalize these results to higher-order
odd-dimensional spheres equipped with their natural subRiemannian structure,
where the limiting spaces are now the higher-dimensional Heisenberg groups.</abstract><doi>10.48550/arxiv.1710.02550</doi><oa>free_for_read</oa></addata></record> |
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| source | arXiv.org |
| subjects | Mathematics - Analysis of PDEs |
| title | Small-time asymptotics for subelliptic Hermite functions on $SU(2)$ and the CR sphere |
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