有限维Hilbert空间中框架的长度手术
Length surgery of frames in finite dimensional Hilbert spaces

针对有限维Hilbert空间中框架的长度手术的操作过程的情况，分别提出了非负实数可以添加进一个紧框架集而成为一个新的紧框架集、紧框架集任意删除p个数、实施(q，q)-长度手术的方法，得到在替换操作中推广了紧框架集上可以实施(q，q)-长度手术而仍然是紧框架集的充要条件的结论.
According the operational procedure of length surgery of in finite dimensional Hilbert spaces，we put forward the method of adding negative real numbers to a tight frame set resulting in a new tight frame set，a tight frame set after deleting random p numbers，and performing a (q，q)-length surgery，respectively，get the conclusion that we generalize the necessary and sufficient condition for keeping a tight frame set under performing a (q，q)-length surgery on a tight frame set in replacing operation