JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (12): 99-104.doi: 10.6040/j.issn.1671-9352.0.2017.505

Previous Articles     Next Articles

Some properties of measure frames

LI Chun-fang, MENG Bin   

  1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Jiangsu Province, Nanjing 210016, Jiangsu, China
  • Online:2018-12-20 Published:2018-12-18

PDF (PC)

352

Abstract: Measure frames is a generalization of vector frames in Hilbert spaces, but there are essential differences between them. Some inequalities and equalities are obtained for measure frames from the perspective of frame operator theory. At the same time, we also discuss the shift of a measure frame to a tight measure frame and the approximately dual frames and pseudo-dual frames.

Key words: measure frames, operator, shift, pseudo-dual

CLC Number: 

  • O177.1
[1] HAN Deguang, LARSON David, LIU Bei. Operator-valued measures, dilations, and the theory of frames[J]. Mem Amer Math Soc, 2014, 229(1075):1-84.
[2] HAN Deguang, LARSON David. Frames, bases, and group representations[J]. Mem Amer Math Soc, 2000, 147(697):1-94.
[3] CHRISTENSON Ole. An introduction to frames and Riesz bases[J]. Birkhauser Boston, 2003, 3(5):59-76.
[4] GABARDO J P, HAN Deguang. Frames associated with measurable space[J]. Adv Comp Math, 2003, 18(2/3/4):127-147.
[5] KAFTAL V, ZHANG Shuang. Operator-valued frames[J]. Trans Amer Math Soc, 2009, 361(12):6349-6385.
[6] SUN Wenchang. G-frames and g-Riesz bases[J]. J Math Anal Appl, 2006, 322(1):439-452.
[7] CASAZZA Peter, KUTYNIOK Gitta, LI Shidong. Fusion frames and distributed processing[J]. Appl Comput Harmon Anal, 2008, 25(1):114-132.
[8] CASAZZA Peter, HAN Deguang, LARSON David. Frames for Banach spaces[J]. Contemp Math, 1999, 82(247):149-182.
[9] FRANK Michael, LARSON David. Frames in Hilbert C*-modules and C*-algebras[J]. Operator Theory, 2002, 48(2):203-233.
[10] GAVRUTA P. On some identities and inequalities for frames in Hilbert spaces[J]. Math Anal Appl, 2006, 321(1):469-478.
[11] EHLER M. Random tight frames[J]. Fourier Anal Appl, 2012, 18(1):1-20.
[12] CHRISTENSEN Ole, LAUGESEN R S. Approximately dual frame pairs in Hilbert space and applications to Gabor frames[J]. Sampling Theroy in Signal & Image Processing, 2010, 9(9):77-89.
[1] TAO Shuang-ping, GAO Rong. Estimates of multilinear fractional integrals and maximal operators on weighted Morrey spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 30-37.
[2] XIN Yin-ping, TAO Shuang-ping. Boundedness of Marcinkiewicz integrals operators with variable kernels on Herz-type Hardy spaces with variable exponent [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 38-43.
[3] . Representative forms of commutative BR0-algebras on a set by implication operator [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(6): 86-94.
[4] PENG Jia-yin. Bidirectional controlled teleportation with a genuine five-qubit non-maximally entangled state as quantum channel [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(12): 105-113.
[5] ZHAO Huan, ZHOU Jiang. Commutators of multilinear Calderón-Zygmund operator on Herz-type Hardy spaces with variable exponent [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2018, 53(10): 42-50.
[6] LU Qiang-de, TAO Shuang-ping. Boundedness of commutators of Calderón-Zygmund operators and fractional integrals in homogeneous grand variable exponent Lebesgue spaces [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(9): 54-58.
[7] ZHANG Qian, LI Hai-yang. The iterative fraction thresholding algorithm in sparse information processing [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(9): 76-82.
[8] WANG Li-li, CHEN Zheng-li. Some research about Wigner-Yanase-Dyson skew information [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(8): 43-47.
[9] LI Li, GUAN Tao, LIN He. The hybrid parallel rough set model based on pansystems operators [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 22-29.
[10] WANG Xia, ZHANG Qian, LI Jun-yu, LIU Qing-feng. Triadic concept analysis based on rough set theory [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(7): 37-43.
[11] YU Wen-jing, BI Dong-xu, YAN Xue-feng. The inpainting of affine similarity damaged image based on structure automatic match [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(3): 32-37.
[12] ZHANG Di, LIU Wen-bin. Existence of solutions for p(t)-Laplacian fractional infinite-point boundary value problems at resonance [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(12): 72-80.
[13] MA Xiao-jie, ZHAO Kai. Boundedness of commutators of the fractional Hardy operators on weighted spaces with variable exponent [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(11): 106-110.
[14] LIU Hui-zhen, XIN Xiao-long, WANG Jun-tao. On derivations of monadic MV-algebras [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(8): 53-60.
[15] REN Chun-nian, GAO Jian. A theory research and experiment scheme on enable-control Anderson localization and delocalization based on quantum walk [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(5): 61-66.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] YANG Jun. Characterization and structural control of metalbased nanomaterials[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2013, 48(1): 1 -22 .
[2] ZHAO Jun1, ZHAO Jing2, FAN Ting-jun1*, YUAN Wen-peng1,3, ZHANG Zheng1, CONG Ri-shan1. Purification and anti-tumor activity examination of water-soluble asterosaponin from Asterias rollestoni Bell[J]. J4, 2013, 48(1): 30 -35 .
[3] SUN Xiao-ting1, JIN Lan2*. Application of DOSY in oligosaccharide mixture analysis[J]. J4, 2013, 48(1): 43 -45 .
[4] LUO Si-te, LU Li-qian, CUI Ruo-fei, ZHOU Wei-wei, LI Zeng-yong*. Monte-Carlo simulation of photons transmission at alcohol wavelength in  skin tissue and design of fiber optic probe[J]. J4, 2013, 48(1): 46 -50 .
[5] YANG Lun, XU Zheng-gang, WANG Hui*, CHEN Qi-mei, CHEN Wei, HU Yan-xia, SHI Yuan, ZHU Hong-lei, ZENG Yong-qing*. Silence of PID1 gene expression using RNA interference in C2C12 cell line[J]. J4, 2013, 48(1): 36 -42 .
[6] MAO Ai-qin1,2, YANG Ming-jun2, 3, YU Hai-yun2, ZHANG Pin1, PAN Ren-ming1*. Study on thermal decomposition mechanism of  pentafluoroethane fire extinguishing agent[J]. J4, 2013, 48(1): 51 -55 .
[7] YANG Ying, JIANG Long*, SUO Xin-li. Choquet integral representation of premium functional and related properties on capacity space[J]. J4, 2013, 48(1): 78 -82 .
[8] LI Yong-ming1, DING Li-wang2. The r-th moment consistency of estimators for a semi-parametric regression model for positively associated errors[J]. J4, 2013, 48(1): 83 -88 .
[9] YANG Yong-wei1, 2, HE Peng-fei2, LI Yi-jun2,3. On strict filters of BL-algebras#br#[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 63 -67 .
[10] ZHAO Tong-xin1, LIU Lin-de1*, ZHANG Li1, PAN Cheng-chen2, JIA Xing-jun1. Pollinators and pollen polymorphism of  Wisteria sinensis (Sims) Sweet[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(03): 1 -5 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd