Construction of the log‐convex minorant of a sequence {Mα}α∈N0d$\lbrace M_\alpha \rbrace _{\alpha \in \mathbb {N}_0^d}$
Abstract We give a simple construction of the log‐convex minorant of a sequence and consequently extend to the ‐dimensional case the well‐known formula that relates a log‐convex sequence to its associated function , that is, . We show that in the more dimensional anisotropic case the classical log‐convex condition is not sufficient: convexity as a function of more variables is needed (not only coordinate‐wise). We finally obtain some applications to the inclusion of spaces of rapidly decreasing ultradifferentiable functions in the matrix weighted setting.
Authors
- Gerhard Schindl (ORCID: https://orcid.org/0000-0003-2192-9110)
- Chiara Boiti (ORCID: https://orcid.org/0000-0001-5027-725X)
- Alessandro Oliaro (ORCID: https://orcid.org/0000-0002-5850-950X)
- David Jornet (ORCID: https://orcid.org/0000-0002-3531-6203)
Institutions
- University of Vienna (AT)
- University of Ferrara (IT)
- University of Turin (IT)
- Universitat Politècnica de València (ES)
Publication Details
- Journal
- Mathematische Nachrichten
- Published
- 2024-11-27
- DOI
- https://doi.org/10.1002/mana.202400135
- Primary Topic
- Mathematical Analysis and Transform Methods
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Austrian Science Fund
- Università degli Studi di Ferrara
- Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni
- European Regional Development Fund
- Agencia Estatal de Investigación