Jiménez-Garrido J, Sanz J, Schindl G. Equality of Ultradifferentiable Classes by Means of Indices of Mixed O-regular Variation.
Results Math 2021;
77:28. [PMID:
34924811 PMCID:
PMC8643302 DOI:
10.1007/s00025-021-01566-4]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/19/2021] [Accepted: 11/14/2021] [Indexed: 06/14/2023]
Abstract
We characterize the equality between ultradifferentiable function classes defined in terms of abstractly given weight matrices and in terms of the corresponding matrix of associated weight functions by using new growth indices. These indices, defined by means of weight sequences and (associated) weight functions, are extending the notion of O-regular variation to a mixed setting. Hence we are extending the known comparison results concerning classes defined in terms of a single weight sequence and of a single weight function and give also these statements an interpretation expressed in O-regular variation.
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