APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

doi:10.1016/S0252-9602(14)60036-9

数学物理学报(英文版) ›› 2014, Vol. 34 ›› Issue (3): 639-652.doi: 10.1016/S0252-9602(14)60036-9

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

Amir KHOSRAVI, Morteza MIRZAEE AZANDARYANI

Faculty of Mathematical Sciences and Computer, Kharazmi (Tarbiat Moallem) University, 599 Taleghani Ave., Tehran 15618, Iran； Faculty of Mathematical Sciences and Computer, Kharazmi (Tarbiat Moallem) University, 599 Taleghani Ave, Tehran 15618, Iran

收稿日期:2012-06-19 修回日期:2013-07-23 出版日期:2014-05-20 发布日期:2014-05-20

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

Amir KHOSRAVI, Morteza MIRZAEE AZANDARYANI

Faculty of Mathematical Sciences and Computer, Kharazmi (Tarbiat Moallem) University, 599 Taleghani Ave., Tehran 15618, Iran； Faculty of Mathematical Sciences and Computer, Kharazmi (Tarbiat Moallem) University, 599 Taleghani Ave, Tehran 15618, Iran

Received:2012-06-19 Revised:2013-07-23 Online:2014-05-20 Published:2014-05-20

摘要/Abstract

摘要：

In this article, we introduce and characterize approximate duality for g-frames. We get some important properties and applications of approximate duals. We also obtain some new results in approximate duality of frames, and generalize some of the known results in approximate duality of frames to g-frames. We also get some results for fusion frames, and perturbation of approximately dual g-frames. We show that approximate duals are stable under small perturbations and they are useful for erasures and reconstruction.

关键词: Frame, g-frame, approximate duality, perturbation, reconstruction

Abstract:

Key words: Frame, g-frame, approximate duality, perturbation, reconstruction

中图分类号:

41A58

Amir KHOSRAVI, Morteza MIRZAEE AZANDARYANI. APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES[J]. 数学物理学报(英文版), 2014, 34(3): 639-652.

Amir KHOSRAVI, Morteza MIRZAEE AZANDARYANI. APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES[J]. Acta mathematica scientia,Series B, 2014, 34(3): 639-652.

参考文献

[1] Asgari M S. Khosravi A. Frames and bases of subspaces in Hilbert spaces. J Math Anal Appl, 2005, 308: 541–553

[2] Balazs P, Feichtinger H G, Hampejs M, Kracher G. Double preconditioning for Gabor frames. IEEE Trans Signal Process, 2006, 54: 4597–4610

[3] Bourouihiya A. The tensor product of frames. Sampling Theory in Signal and Image Process, 2008, 7(1): 65–76

[4] Casazza P, Balan R, Edidin D, Kutyniok G. Decompositions of frames and a new frame identity. SPIE Wavelets Applications in Signal and Image Processing XI, 2005, 5914: 379–388

[5] Casazza P, Kutyniok G. Frames of subspaces. Contemp Math Amer Math Soc, 2004, 345: 87–113

[6] Casazza P, Kutyniok G. Robustness of fusion frames under erasures of subspaces and of local frame vectors.
Contemp Math Amer Math Soc, 2008, 464: 149–160

[7] Casazza P, Kutyniok G, Li S. Fusion frames and distributed processing. Appl Comput Harmon Anal, 2008, 25: 114–132

[8] Christensen O. Frames and bases. An introductory course. Boston: Birkh¨auser, 2008

[9] Christensen O, Laugesen R S. Approximate dual frames in Hilbert spaces and applications to Gabor frames.
Sampling Theory in Signal and Image Processing, 2011, 9: 77–90

[10] Daubechies I, Grossmann A, Meyer Y. Painless nonorthogonal expansions. J Math Phys, 1986, 27: 1271–1283

[11] Duffin R J, Schaeffer A C. A class of nonharmonic Fourier series. Trans Amer Math Soc, 1952, 72: 341–366

[12] Gavruta P. On the duality of fusion frames. J Math Anal Appl, 2007, 333: 871–879

[13] Gilbert J E, Han Y S, Hogan J A, et al. Smooth molecular decompositions of functions and singular integral
operators. Mem Amer Math Soc, 2002, 742: 1–74

[14] Khosravi A, Khosravi B. Frames and bases in tensor products of Hilbert spaces and Hilbert C-modules. Proc Indian Acad Sci (Math Sci), 2007, 117 (1): 1–12

[15] Khosravi A, Khosravi B. Fusion frames and g-frames in Hilbert C-modules. Int J Wavelets Multiresolut Inf Process, 2008, 6: 433–446

[16] Khosravi A, Khosravi B. Fusion frames and g-frames in Banach spaces. Proc Indian Acad Sci (Math Sci), 2011, 121 (2): 155–164

[17] Khosravi A, Mirzaee Azandaryani M. G-frames and direct sums. Bull Malays Math Soc (2), 2013, 36 (2): 313–323

[18] Khosravi A, Musazadeh K. Fusion frames and g-frames. J Math Anal Appl, 2008, 342: 1068–1083

[19] Murphy G J. C-algebra and operator theory. San Diego: Academic Press, 1990

[20] Obeidat S, Samarah S, Casazza P, Tremain J C. Sums of Hilbert space frames. J Math Anal Appl, 2009, 351: 579–585

[21] Sun W. G-frames and g-Riesz bases. J Math Anal Appl, 2006, 322: 437–452

[22] Werther T, Eldar Y C, Subbanna N K. Dual Gabor frames: theory and computational aspects. IEEE Trans Signal Process, 2005, 53: 4147–4158

[23] Xiao X C, Zeng X M. Some equalities and inequalities of g-continuous frames. Sci China Ser A, 2010, 53(10): 2621–2632

[24] Zhu Y C. Characterizations of g-frames and g-Riesz bases in Hilbert spaces. Acta Math Sinica, English Series, 2008, 24 (10): 1727–1736

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

APPROXIMATE DUALITY OF g-FRAMES IN HILBERT SPACES

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 10

[1]	陈贵强, Matthew RIGBY. STABILITY OF STEADY MULTI-WAVE CONFIGURATIONS FOR THE FULL EULER EQUATIONS OF COMPRESSIBLE FLUID FLOW[J]. 数学物理学报(英文版), 2018, 38(5): 1485-1514.
[2]	唐少君, 张澜. NONLINEAR STABILITY OF VISCOUS SHOCK WAVES FOR ONE-DIMENSIONAL NONISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH A CLASS OF LARGE INITIAL PERTURBATION[J]. 数学物理学报(英文版), 2018, 38(3): 973-1000.
[3]	王紫, 王玉文. A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES[J]. 数学物理学报(英文版), 2017, 37(6): 1619-1631.
[4]	Teresa ÁLVAREZ. LEFT-RIGHT BROWDER LINEAR RELATIONS AND RIESZ PERTURBATIONS[J]. 数学物理学报(英文版), 2017, 37(5): 1437-1452.
[5]	Alberto CABADA, Nikolay D. DIMITROV. EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS[J]. 数学物理学报(英文版), 2017, 37(4): 911-926.
[6]	Nai-Sher YEH, Chung-Cheng KUO. MULTIPLICATIVE PERTURBATIONS OF LOCAL α-TIMES INTEGRATED C-SEMIGROUPS[J]. 数学物理学报(英文版), 2017, 37(3): 877-888.
[7]	谌稳固, 李亚玲. STABLE RECOVERY OF SIGNALS WITH THE HIGH ORDER D-RIP CONDITION[J]. 数学物理学报(英文版), 2016, 36(6): 1721-1730.
[8]	武利猛, 张娟, 倪明康, 陆海波. ASYMPTOTIC SOLUTION OF SINGULARLY PERTURBED HYBRID DYNAMICAL SYSTEMS[J]. 数学物理学报(英文版), 2016, 36(5): 1457-1466.
[9]	Kamran MUSAZADEH, Hassan KHANDANI. SOME RESULTS ON CONTROLLED FRAMES IN HILBERT SPACES[J]. 数学物理学报(英文版), 2016, 36(3): 655-665.
[10]	Laura GAVRUTA, Pasc GAVRUTA. SOME PROPERTIES OF OPERATOR-VALUED FRAMES[J]. 数学物理学报(英文版), 2016, 36(2): 469-476.
[11]	Chung-Cheng KUO. ADDITIVE PERTURBATIONS OF LOCAL C-SEMIGROUPS[J]. 数学物理学报(英文版), 2015, 35(6): 1566-1576.
[12]	Salma CHARFI, Sassia RAHALI. ON A CHARACTERIZATION OF THE S-ESSENTIAL SPECTRA OF THE SUM AND THE PRODUCT OF TWO OPERATORS AND APPLICATION TO A TRANSPORT OPERATOR[J]. 数学物理学报(英文版), 2015, 35(6): 1285-1304.
[13]	Ufuk OZTURK, Suleyman CENGIZ, Esra Betul KOC OZTURK. MOTIONS OF CURVES IN THE GALILEAN SPACE G₃[J]. 数学物理学报(英文版), 2015, 35(5): 1046-1054.
[14]	Aymen AMMAR, Bilel BOUKETTAYA, Aref JERIBI. STABILITY OF THE S-LEFT AND S-RIGHT ESSENTIAL SPECTRA OF A LINEAR OPERATOR[J]. 数学物理学报(英文版), 2014, 34(6): 1922-1934.
[15]	卢春\|丁效华. PERSISTENCE AND EXTINCTION OF A STOCHASTIC LOGISTIC MODEL WITH DELAYS AND IMPULSIVE PERTURBATION[J]. 数学物理学报(英文版), 2014, 34(5): 1551-1570.