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ВИДЕОТЕКА |
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Gabor frames for rational functions Yu. S. Belov Saint-Petersburg State University, Department of Mathematics and Computer Science |
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Аннотация: Let $$G(g,\alpha,\beta)=\{e^{2\pi i \alpha m x}g(x-\beta n)\}_{m,n\in\mathbb{Z}}.$$ The main question of Gabor analysis is to describe frame set, i.e. to describe pairs Up to now it was known only few functions We managed to find a new class of functions with complete description of frame set – rational functions of Herglotz type. This was done by combination of classical theory of entire functions with some ideas from dynamical systems. We also proved some other results for arbitrary rational functions and some results for non-lattice Gabor systems. The talk is based on joint works with A. Kulikov and Yu. Lyubarskii. |