Construction of the log-convex minorant of a sequence {M_alpha}_alpha
[EN] We give a simple construction of the log-convex minorant of a sequence {M_alpha}_alpha and consequently extend to the d-dimensional case the well-known formula that relates a log-convex sequence {M_p} to its associated function omega(M), that is M_p=sup(t>0)t(p)exp(-omega(M)(t)). We show...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de València (UPV) |
| Repositorio: | RiuNet. Repositorio Institucional de la Universitat Politécnica de Valéncia |
| Idioma: | inglés |
| OAI Identifier: | oai:riunet.upv.es:10251/213363 |
| Acceso en línea: | https://riunet.upv.es/handle/10251/213363 |
| Access Level: | acceso abierto |
| Palabra clave: | Log-convex sequences Matrix weights Regularization of sequences Ultradifferentiable functions MATEMATICA APLICADA |
| Sumario: | [EN] We give a simple construction of the log-convex minorant of a sequence {M_alpha}_alpha and consequently extend to the d-dimensional case the well-known formula that relates a log-convex sequence {M_p} to its associated function omega(M), that is M_p=sup(t>0)t(p)exp(-omega(M)(t)). We show that in the more dimensional anisotropic case the classical log-convex condition M-alpha(2)<= M alpha-ejM alpha+ej 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. |
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