Sampling multipliers and the Poisson Summation Formula
| العنوان: | Sampling multipliers and the Poisson Summation Formula |
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| المؤلفون: | Georg Zimmermann, John J. Benedetto |
| المصدر: | The Journal of Fourier Analysis and Applications. 3:505-523 |
| بيانات النشر: | Springer Science and Business Media LLC, 1997. |
| سنة النشر: | 1997 |
| مصطلحات موضوعية: | Pure mathematics, Summation by parts, Discrete-time Fourier transform, Applied Mathematics, General Mathematics, Poisson summation formula, Sampling (statistics), Borel summation, Summation equation, Algebra, symbols.namesake, Operator (computer programming), symbols, Summation of Grandi's series, Analysis, Mathematics |
| الوصف: | Periodization and sampling operators are defined, and the Fourier transform of periodization is uniform sampling in a well-defined sense. Implementing this point of view, Poisson Summation Formulas are proved in several spaces including integrable functions of bounded variation (where the result is known) and elements of mixed norm spaces. These Poisson Summation Formulas can be used to prove corresponding sampling theorems. The sampling operators used to understand and prove the aforementioned Poisson Summation Formulas lead to the introduction of spaces of continuous linear operators which commute with integer translations. Operators L of this type are appropriately called sampling multipliers. For a given function f, they give rise to new sampling formulas, whose sampling coefficients are of the form Lf. In practice, Lf can be used to model noisy data or data where point values are not available. By representation theorems of the second named author, some of these operator spaces are proved to be mixed norm spaces. The approach and results of this paper were developed in the context of Duffin and Schaeffer’s theory of frames. In particular, sampling multipliers L are related to the Bessel map used by Duffin and Schaeffer in their definition of the frame operator. |
| تدمد: | 1531-5851 1069-5869 |
| الوصول الحر: | https://explore.openaire.eu/search/publication?articleId=doi_________::6babb01eb1df75207ecd3476ff0bcb73Test https://doi.org/10.1007/bf02648881Test |
| حقوق: | CLOSED |
| رقم الانضمام: | edsair.doi...........6babb01eb1df75207ecd3476ff0bcb73 |
| قاعدة البيانات: | OpenAIRE |
| تدمد: | 15315851 10695869 |
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