Abstract
AbstractWe prove that the Hermite functions are an absolute Schauder basis for many global weighted spaces of ultradifferentiable functions in the matrix weighted setting and we determine also the corresponding coefficient spaces, thus extending the previous work by Langenbruch. As a consequence, we give very general conditions for these spaces to be nuclear. In particular, we obtain the corresponding results for spaces defined by weight functions.
Funder
Ministero dell’Istruzione, dell’Università e della Ricerca
Università degli Studi di Ferrara
Generalitat Valenciana
Ministerio de Economía, Industria y Competitividad, Gobierno de España
Austrian Science Fund
Publisher
Springer Science and Business Media LLC
Subject
Algebra and Number Theory,Analysis
Reference41 articles.
1. Asensio, V., Jornet, D.: Global pseudodifferential operators of infinite order in classes of ultradifferentiable functions. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(4), 3477–3512 (2019)
2. Aubry, J.-M.: Ultrarapidly decreasing ultradifferentiable functions, Wigner distributions and density matrices. J. Lond. Math. Soc. 2(78), 392–406 (2008)
3. Björck, G.: Linear partial differential operators and generalized distributions. Ark. Mat. 6(21), 351–407 (1966)
4. Bierstedt, K.D., Bonet, J.: Some aspects of the modern theory of Fréchet spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 97(2), 159–188 (2003)
5. Bierstedt, K.D., Meise, R.: Distinguished echelon spaces and the projective description of weighted inductive limits of type $${\cal{V}} _{d}\cal{C} (X)$$. In: Aspects of Mathematics and Its Applications. North-Holland Mathematics Library, Amsterdam, vol. 34, pp. 169–226 (1986)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. On the Inclusion Relations of Global Ultradifferentiable Classes Defined by Weight Matrices;Mediterranean Journal of Mathematics;2024-07-08
2. The Borel map in the mixed Beurling setting;Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas;2022-12-12
3. Global Wave Front Sets in Ultradifferentiable Classes;Results in Mathematics;2022-02-02