{"product_id":"9781470420154","title":"abc-Problem for Gabor Systems","description":"A longstanding problem in Gabor theory is to identify time-frequency shifting lattices $a\\mathbb{Z}\\times b\\mathbb{Z}$ and ideal window functions $\\chiI$ on intervals $I$ of length $c$ such that $\\{e^{-2\\pi i n bt} \\chiI(t- m a):\\ (m, n)\\in \\mathbb{Z}\\times \\mathbb{Z}\\}$ are Gabor frames for the space of all square-integrable functions on the real line. In this paper, the authors create a time-domain approach for Gabor frames, introduce novel techniques involving invariant sets of non-contractive and non-measure-preserving transformations on the line, and provide a complete answer to the above $abc$-problem for Gabor systems.","brand":"Xin-Rong Dai","offers":[{"title":"Default Title","offer_id":46776516542782,"sku":"9781470420154","price":0.0,"currency_code":"ZAR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9781470420154_fed3a4a3-27a4-4d0c-a211-7230df31686a.jpg?v=1707476979","url":"https:\/\/exclusivebooks.co.za\/products\/9781470420154","provider":"Exclusive Books Online","version":"1.0","type":"link"}