本文關(guān)鍵詞：G-框架的若干問題研究，由筆耕文化傳播整理發(fā)布。

網(wǎng)友Alphago近日為您收集整理了關(guān)于G-框架的若干問題研究的文檔，希望對您的工作和學(xué)習(xí)有所幫助。以下是文檔介紹： of g- orthonormal basesfor expanding a r b i t r a r y elements, in addition, approximately dual g- frames and g- dualg- frames could break t hrough the l i m i t a t i o n s of dual g- frames. So, on the one hand, inthis thesis, we study the necessary and sufficient condition for the fi n i t e extension t o at i g h t g- frame o f a g- frame in an infinite-dimensional H i l b e r t space and several equivalentconditions for a g- frame i n a H i l b e r t space t o be scalable, where the scalable g- frameis a g- frame which can generate a Parseval g- frame by rescaling its frame elements, onthe other hand, we introduce the concepts of approximately dual g- frames and g- dualg- frames, f ind t h e i r properties and perturbations. A t last, we characterize all g- dual g-frames of a given frame i n a H i l b e r t space. The thesis consists o f six chapters.Chapter 1 introduces the background o f frames and g- frames and the structure andwork o f the thesis.Chapter 2 lists the concept and some basic facts of g- frames and the properties oflinear bounded operators in a H i l b e r t space t hroughout the thesis.Chapter 3 is one o f the main contents. The necessary and sufficient conditions forthe fi n i t e extension t o a t i g h t g- frame of a g- Bessel sequence and g- frame in an i n f i n i t e -dimensional H i l b e r t space are given.Chapter 4 is the second work. I n this chapter several equivalent conditions for a g-frame in a H i l b e r t space t o be scalable are provided.IIIG- 框架的若干問題研究Chapter 5 introduces the concept of approximately dual g- frames and studies t h e i rproperties and perturbations.The final p a r t is chapter 6. Fir s t ly , the definition o f g- dualand then the properties and perturbations of g- dual g- framescharacterization o f g- dual g- frames is established.g- frames is presented,are given. Finally, theK E Y W O R D S: g- Bessel sequence, g- frame, t i g h t g- frame,frame, g- dual g- frameapproximately dual g-IV

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  本文關(guān)鍵詞：G-框架的若干問題研究，由筆耕文化傳播整理發(fā)布。