Generalized frames and their redundancy

Gabor frames with reduced redundancy

(1) Department of Mathematics, Technical University of Denmark, Building 303, 2800 Lyngby, Denmark. (2) Department of Mathematical Sciences, KAIST, Daejeon, Korea. (3) Department of Mathematics, Yeungnam University, Gyeongsan-si,Korea. [email protected], [email protected], [email protected] This work was supported by the Korea Science and Engineering Foundation (KOSEF) Grant funded by th...

Similar generalized frames

Generalized frames are an extension of frames in Hilbert  spaces and  Hilbert $C^*$-modules. In this paper, the concept ''Similar" for modular $g$-frames is introduced and all of operator duals (ordinary duals) of similar $g$-frames with respect to each other are characterized. Also, an operator dual of a given $g$-frame is studied where $g$-frame is constructed by a primary $g$-frame and an or...

Generalized Frames in Hilbert Spaces

افزونگی قاب های موضعی (redundancy for localized frames)

نشان میدهیم افزونگی یک ویژگی کیفی است که قاب های فضای هیلبرت را در کاربرد مفید می سازد. با این حال بدست آوردن یک تعریف کمی معنی دار از افزونگی برای قاب های نامتناهی پیچیده است ولی از آن جایکه جایگزین هایی برای افزونگی موجود است مهمترین مساله باز این است که ایا یک قاب با افزونگی بزرگتر از یک دارای یک زیر قاب با افزونگی دلخواه نزدیک به 1 هست یا نه ؟ ما به این سوال برای قاب های موضعی شده جواب مثب...

Generalized Continuous Frames for Operators

In this note, the notion of generalized continuous K- frame in a Hilbert space is defined. Examples have been given to exhibit the existence of generalized continuous $K$-frames. A necessary and sufficient condition for the existence of a generalized continuous $K$-frame in terms of its frame operator is obtained and a characterization of a generalized continuous $K$-frame for $ mathcal{H} $ wi...