Frame Potential of Dual Frames and Phase Retrievable Frames

被引：0
作者：
Jafarizadeh, M. [1 ]
Fard, M. A. Hasankhani [1 ]
机构：
[1] Vali e Asr Univ Rafsanjan, Rafsanjan, Iran
来源：
JOURNAL OF CONTEMPORARY MATHEMATICAL ANALYSIS-ARMENIAN ACADEMY OF SCIENCES | 2024年 / 59卷 / 06期
关键词：
frame; dual frame; frame potential; phase retrievable frame; norm retrievable frame; RECONSTRUCTION;
D O I：
10.3103/S1068362324700377
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper is concentrated on the frame potential of finite frames in n-dimensional Hilbert space H-n. More precisely, We define the relative frame potential of two sequences F and G in H-n, which is denoted by (FP) over tilde (F, G). For dual frames F and G in H-n, we show that G is canonical dual frame of F if and only (FP) over tilde (F, G) = n. A lower and upper bound for (FP) over tilde (F, G) is given, for the case that F and G are frames for H-n. Also, using the relative frame potential of the sub sequences of a given frame, some equivalent conditions for its phase retrievability and its norm retrievability, are presented.
引用
收藏
页码：409 / 418
页数：10
相关论文
共 18 条
  • [1] Duffin R.J., Schaeffer A.C., A class of nonharmonic Fourier series, Trans. Am. Math. Soc, 72, pp. 341-366, (1952)
  • [2] Casazza P.G., Leon M.T., Existence and construction of finite tight frames, Journal of Concrete and Applicable Mathematics, 4, pp. 277-289, (2006)
  • [3] Casazza P.G., Leon M., Existence and construction of finite frames with a given frame operator, Int. J. Pure Appl. Math, 63, pp. 149-158, (2010)
  • [4] Benedetto J.J., Wavelets: Mathematics and Applications, (1999)
  • [5] Christensen O., An Introduction to Frames and Riesz Bases, (2002)
  • [6] Heil C.E., Walnut D.F., Continuous and discrete wavelet transforms, SIAM Rev, 31, pp. 628-666, (1969)
  • [7] Sun W., G-frames and g-Riesz bases, J. Math. Anal. Appl, 322, pp. 437-452, (2006)
  • [8] Young R., An Introduction to Nonharmonic Fourier Series, (1992)
  • [9] Benedetto J., Fickus M., Finite normalized tight frames, Adv. Comput. Math, 18, pp. 357-385, (2003)
  • [10] Balan R., Casazza P., Edidin D., On signal reconstruction without phase, Appl. Comput. Harmonic Anal, 20, pp. 345-356, (2006)
12