Vector Valued Gårding Inequality for pseudo-differential operators on compact homogeneous manifolds
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| Format: | Preprint |
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2024
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| _version_ | 1866914729100836864 |
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| author | Kowacs, André Ruzhansky, Michael |
| author_facet | Kowacs, André Ruzhansky, Michael |
| contents | We prove sufficient conditions in order to obtain a sharp Gårding inequality for pseudo-differential operators acting on vector-valued functions on compact Lie groups. As a consequence, we obtain a sharp Gårding inequality for compact homogeneous vector bundles and compact homogeneous manifolds. The sharp Gårding inequality is the strongest lower bound estimate known to hold for systems on $\mathbb{R}^n$, and the aim of this paper is to extend this property to systems on compact Lie groups and compact homogeneous manifolds. Our results extend previous works by Lax and Nirenberg [Comm. Pure Appl. Math., Vol. 8, 129-209, (1966)], and by Ruzhansky and Turunen [J. Funct. Anal., Vol. 267, 144-172, (2011)]. As an application, we establish existence and uniqueness of solution to a class of systems of initial value problems of pseudo-differential equations on compact Lie groups and compact homogeneous manifolds. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_18966 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Vector Valued Gårding Inequality for pseudo-differential operators on compact homogeneous manifolds Kowacs, André Ruzhansky, Michael Analysis of PDEs Primary 22E30, 43A77. Secondary 58J40, 35S10 We prove sufficient conditions in order to obtain a sharp Gårding inequality for pseudo-differential operators acting on vector-valued functions on compact Lie groups. As a consequence, we obtain a sharp Gårding inequality for compact homogeneous vector bundles and compact homogeneous manifolds. The sharp Gårding inequality is the strongest lower bound estimate known to hold for systems on $\mathbb{R}^n$, and the aim of this paper is to extend this property to systems on compact Lie groups and compact homogeneous manifolds. Our results extend previous works by Lax and Nirenberg [Comm. Pure Appl. Math., Vol. 8, 129-209, (1966)], and by Ruzhansky and Turunen [J. Funct. Anal., Vol. 267, 144-172, (2011)]. As an application, we establish existence and uniqueness of solution to a class of systems of initial value problems of pseudo-differential equations on compact Lie groups and compact homogeneous manifolds. |
| title | Vector Valued Gårding Inequality for pseudo-differential operators on compact homogeneous manifolds |
| topic | Analysis of PDEs Primary 22E30, 43A77. Secondary 58J40, 35S10 |
| url | https://arxiv.org/abs/2402.18966 |