Finite Frame Theory

2016 ◽  
Keyword(s):  
Frame Theory ◽  
Finite Frame

Parseval transforms for finite frames

2018 ◽  
Vol 16 (03) ◽  
pp. 1850014 ◽  
Author(s):  
Xianwei Zheng ◽  
Shouzhi Yang ◽  
Yuan Yan Tang ◽  
Youfa Li
Keyword(s):  
Frame Theory ◽  
Square Root ◽  
Graph Structure ◽  
Finite Frames ◽  
Frame Operator ◽  
Finite Frame ◽  
Parseval Frames ◽  
Schmidt Orthogonalization ◽  
The Right ◽  
The Relationship

The relationship between frames and Parseval frames is an important topic in frame theory. In this paper, we investigate Parseval transforms, which are linear transforms turning general finite frames into Parseval frames. We introduce two classes of transforms in terms of the right regular and left Parseval transform matrices (RRPTMs and LPTMs). We give representations of all the RRPTMs and LPTMs of any finite frame. Two important LPTMs are discussed in this paper, the canonical LPTM (square root of the inverse frame operator) and the RGS matrix, which are obtained by using row’s Gram–Schmidt orthogonalization. We also investigate the relationship between the Parseval frames generated by these two LPTMs. Meanwhile, for RRPTMs, we verify the existence of invertible RRPTMs for any given finite frame. Finally, we discuss the existence of block diagonal RRPTMs by taking the graph structure of the frame elements into consideration.

Introduction to Finite Frame Theory

Finite Frames ◽  
2013 ◽  
pp. 1-53 ◽  
Author(s):  
Peter G. Casazza ◽  
Gitta Kutyniok ◽  
Friedrich Philipp
Keyword(s):  
Frame Theory ◽  
Finite Frame

scholarly journals Continuous ⁎-K-G-Frame in Hilbert C⁎-Modules

2019 ◽  
Vol 2019 ◽  
pp. 1-5
Author(s):  
Mohamed Rossafi ◽  
Abdeslam Touri ◽  
Hatim Labrigui ◽  
Abdellatif Akhlidj
Keyword(s):  
Frame Theory

Frame theory is exciting and dynamic with applications to a wide variety of areas in mathematics and engineering. In this paper, we introduce the concept of Continuous ⁎-K-g-frame in Hilbert C⁎-Modules and we give some properties.

scholarly journals Evaluating the evidence base for relational frame theory: A citation analysis

2010 ◽  
Vol 33 (1) ◽  
pp. 97-117 ◽  
Author(s):  
Simon Dymond ◽  
Richard J. May ◽  
Anita Munnelly ◽  
Alice E. Hoon
Keyword(s):  
Citation Analysis ◽  
Relational Frame Theory ◽  
Evidence Base ◽  
Frame Theory ◽  
Relational Frame
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