TY - GEN A1 - Kutyniok, Gitta A1 - Okoudjou, Kasso A. A1 - Philipp, Friedrich A1 - Tuley, Elizabeth K. T1 - Scalable Frames N2 - Tight frames can be characterized as those frames which possess optimal numerical stability properties. In this paper, we consider the question of modifying a general frame to generate a tight frame by rescaling its frame vectors; a process which can also be regarded as perfect preconditioning of a frame by a diagonal operator. A frame is called scalable, if such a diagonal operator exists. We derive various characterizations of scalable frames, thereby including the infinite-dimensional situation. Finally, we provide a geometric interpretation of scalability in terms of conical surfaces. KW - Conical surfaces KW - Diagonal operator KW - Preconditioner KW - Tight frames Y1 - 2012 UR - https://opus4.kobv.de/opus4-matheon/frontdoor/index/index/docId/1159 UR - https://nbn-resolving.org/urn:nbn:de:0296-matheon-11597 ER -