A restriction theorem for Grushin operators |
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Authors: | Heping Liu Manli Song |
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Affiliation: | 1. School of Mathematical Sciences, Peking University, Beijing 100871, China2. School of Natural and Applied Sciences, Northwestern Polytechnical University, Xi’an 710129, China |
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Abstract: | We study the Grushin operators acting on \(\mathbb{R}_x^{{d_1}} \times \mathbb{R}_t^{{d_2}}\) and defined by the formula \(L = - \sum\nolimits_{j = 1}^{{d_1}} {\partial _{{x_j}}^2} - {\sum\nolimits_{j = 1}^{{d_1}} {\left| {{x_j}} \right|} ^2}\sum\nolimits_{k = 1}^{{d_2}} {\partial _{{t_k}}^2} \). We establish a restriction theorem associated with the considered operators. Our result is an analogue of the restriction theorem on the Heisenberg group obtained by D. M¨uller Ann. of Math., 1990, 131: 567–587]. |
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Keywords: | Grushin operator scaled Hermite operator restriction operator |
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