Abstract
We seek to characterise, in simple and unsophisticated terms, frame operators of Weyl–Heisenberg frames. We succeed only partially, using the newly introduced concepts of window operators and tile vertices. However, we are able to completely characterise the frame operator in each of two newly introduced classes: window Weyl–Heisenberg frames (a special class of Weyl–Heisenberg frames) and generalised Weyl–Heisenberg frames (a class more general than Weyl–Heisenberg frames). Nous cherchons à caractériser, dans les termes simples, opérateurs des repères de Weyl–Heisenberg. Nous succédons seulement partiellement, en utilisant les concepts, nouvellement introduits, des opérateurs de fenètre et de vertices de tuile. Pourtant, nous pouvons caractériser complètement les opérateurs dans chacune de deux classes nouvellement présentées : repères de fenètre Weyl–Heisenberg (une classe spéciale de repères de Weyl–Heisenberg) et repères de généralisé Weyl–Heisenberg (une classe plus générale que repères de Weyl–Heisenberg).
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