Linear combinations of frames and frame packets
The author finds coefficients \(c_{mn}\) (\(m, n \in Z\)) such that for an arbitrary frame \(\{f_n\}_{n \in Z}\) the set of vectors \(\{\varphi_m\}_{m \in Z} = \{\sum_{n \in Z} c_{mn}f_n\}_{m \in Z}\) will again be a frame. Appropriate coefficients can always be chosen as function values \(c_{mn} = g({n \over \beta}-m\alpha)\), where \(g\) belongs to a broad class of functions generating a Gabor frame \(\{E_{\beta m}T_{\alpha n}g\}_{m, n \in Z}\) for \(L^2(R)\). He also proves a version of the splitting trick, which allows for the construction of a large family of frames based on a single (wavelet or Gabor) frame.
scientific article; zbMATH DE number 1747391