On global inversion of homogeneous maps

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• 作者：Michael Ruzhansky ; Mitsuru Sugimoto
• 关键词：Inverse function theorem ; Homogeneous mappings ; Global inverse ; Primary 26B10 ; Secondary 26B05 ; 26 ; 01
• 刊名：Bulletin of Mathematical Sciences
• 出版年：2015
• 出版时间：April 2015
• 年：2015
• 卷：5
• 期：1
• 页码：13-18
• 全文大小：120 KB
• 参考文献：1. Asada, K, Fujiwara, D (1978) On some oscillatory integral transformations in $$L^{2}({ R}^{n})$$ L 2 ( R n ). Jpn. J. Math. 4: pp. 299-361
  2. Gordon, WB (1972) On the diffeomorphisms of Euclidean space. Am. Math. Mon. 79: pp. 755-759 CrossRef
  3. Hadamard, J.: Sur les correspondances ponctuelles. Paris: Oeuvres, Editions du Centre Nationale de la Researche Scientifique, pp. 383-84 (1998)
  4. Hadamard, J (1906) Sur les transformations planes. C. R. Math. Acad. Sci. Paris 142: pp. 74
  5. Hadamard, J (1906) Sur les transformations ponctuelles. Bull. Soc. Math. Fr. 34: pp. 71-84
  6. Nijenhuis, A, Richardson, RW (1962) A theorem on maps with non-negative Jacobians. Mich. Math. J. 9: pp. 173-176 CrossRef
  7. Ruzhansky, M, Sugimoto, M (2006) Global $$L^2$$ L 2 -boundedness theorems for a class of Fourier integral operators. Commun. Partial Differ. Equ. 31: pp. 547-569 CrossRef
  8. Ruzhansky, M, Sugimoto, M (2006) A smoothing property of Schr?dinger equations in the critical case. Math. Ann. 335: pp. 645-673 CrossRef
  
• 刊物主题：Mathematics, general;
• 出版者：Springer Basel
• ISSN：1664-3615

文摘

In this note we prove a global inverse function theorem for homogeneous mappings on \({\mathbb R}^n\) . The proof is based on an adaptation of the Hadamard’s global inverse theorem which provides conditions for a function to be globally invertible on \({\mathbb R}^n\) . For the latter adaptation, we give a short elementary proof assuming a topological result.