On the local integrability condition for generalised translation-invariant systems
| Autor: | Jordy Timo van Velthoven |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Relation (database) Applied Mathematics General Mathematics The Intersect 010102 general mathematics 05 social sciences Translation (geometry) 01 natural sciences Functional Analysis (math.FA) Mathematics - Functional Analysis Compact space 42C40 43A32 42C15 43A70 0502 economics and business FOS: Mathematics 0101 mathematics Invariant (mathematics) 050203 business & management Mathematics |
| DOI: | 10.48550/arxiv.1801.08378 |
| Popis: | This paper considers the local integrability condition for generalised translation-invariant systems and its relation to the Calder\'on integrability condition, the temperateness condition and the uniform counting estimate. It is shown that sufficient and necessary conditions for satisfying the local integrability condition are closely related to lower and upper bounds on the number of lattice points that intersect with the translates of a compact set. The results are complemented by examples that illustrate the crucial interplay between the translation subgroups and the generating functions of the system. Comment: Minor revision. To appear in Collect. Math |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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