Function spaces obeying a time-varying bandlimit
| Autor: | Robert T. W. Martin, Achim Kempf |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Bandlimiting
Pure mathematics Signal processing Variables Function space Applied Mathematics media_common.quotation_subject 010102 general mathematics 020206 networking & telecommunications 02 engineering and technology Hardy space 01 natural sciences Linear map symbols.namesake 0202 electrical engineering electronic engineering information engineering symbols 0101 mathematics Real line Analysis Mathematics Meromorphic function media_common |
| Zdroj: | Journal of Mathematical Analysis and Applications. 458:1597-1638 |
| ISSN: | 0022-247X |
| DOI: | 10.1016/j.jmaa.2017.10.018 |
| Popis: | Motivated by applications to signal processing and mathematical physics, recent work on the concept of time-varying bandwidth has produced a class of function spaces which generalize the Paley–Wiener spaces of bandlimited functions: any regular simple symmetric linear transformation with deficiency indices ( 1 , 1 ) is naturally represented as multiplication by the independent variable in one of these spaces. We explicitly demonstrate the equivalence of this model for such linear transformations to several other functional models based on the theories of meromorphic model spaces of Hardy space and purely atomic Herglotz measures on the real line, respectively. This theory provides a precise notion of a time-varying or local bandwidth, and we describe how it may be applied to construct signal processing techniques that are adapted to signals obeying a time-varying bandlimit. |
| Databáze: | OpenAIRE |
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