Publications

Recent Acknowledgements:

                         

Research papers

2021-2025

  1. Zero-error correctibility and phase retrievability for twirling channels (with Kai Liu), Reports on Mathematical Physics, 93(2024), 87-102.
  2. Dilations for operator-valued quantum measures (with Q. Hu, A. Larson and R. Liu), Advances in Mathematics., 438(2024), 109476.
  3. Determination of compactly supported functions in shift-invariant space by single-angle Radon samples (with S. Fan and Y. Li), J. Funct. Anal.,  285(2023), 110151
  4. The uniqueness of phase retrieval of analytic signals from very few STFT measurements,(with Y. Li and H. Wang), Circuits, Systems, and Signal Processing, 43(2024), 2507-2532
  5. Orbit-injective covariant quantum channels (with and C. Cheng and K. Liu), Linear Alg. Appl., 668 (2023), 28–50.
  6. Generalized Choi-Kraus dilations of linear maps between matrix algebras (with Q. Hu and R. Liu),  Oper. Matrices 16 (2022), no. 4, 1219–1237
  7. Quantum injectivity of multi-window Gabor frames in finite dimensions (with Q. Hu, R. Liu and H. Wang). Ann. Funct. Anal. 13 (2022), no. 4, Paper No. 59, 17 pp.
  8. FROG-measurement based phase retrieval for analytic signals (with Y. Li and Y. Ma), Appl. Comput. Harm. Anal., 55(2021), 199-222
  9. Gabor single-frame and multi-frame multipliers in any given dimension (with Y. Diao and Z. Li),  J. Funct. Anal. ,   280(2021), 108960
  10. Nonuniform sampling and approximation in Sobolev spaces from perturbations of framelet systems (with Y. Li etc).  Sciences in China – Mathematics, 64(2021), 351-372
  11. Injective continuous frames and quantum detections (with Q. Hu, R. Liu),  Banach J. Math. Anal., 15 (1) (2021), 1-24

2016-2020

  1. A duality principle for groups II: Multi-frames meet super-frames  (with R. Balan, D. Dutkay, D. Larson, F. Luef),  Journal of Fourier Anal. Appl.,   26 (6) (2020), 1-19
  2. Erasure recovery matrices for encoder protection (with D. Larson, S. Scholze and W. Sun), Appl. Comput. Harm. Anal., 48(2020), 766-786
  3. Structural properties of homomorphism dilation systems (with D. Larson and  R. Liu ), Chinese Annals of Mathematics Ser.B, 41(2020), 585-600.
  4. Frames and Finite-Rank Integral Representations of Positive Operator-Valued Measures (with J-P. Gabardo), Acta Appl. Math.,166(2020), 11-27.
  5. Frame Phase-Retrievability and Exact Phase-Retrievable Frames (with T. Juste, Y. Li and W. Sun),  J. Fourier Anal. Appl., 25(2019), 3154–3173
  6. Phase-retrievable operator-valued frames and representations of quantum channels (with Ted Juste),   Lin. Alg. Appl., 579(2019), 148–168.
  7. Phase retrievable projective representation frames for finite abelian groups ( J. Brennan and C. Cheng , T. Juste and L. Li),  J. Fourier Anal. Appl.,  25(2019), 86-100.
  8. Functional matrix multipliers for Parseval Gabor multi-frame generators (with Z. Li), Acta Appl. Math., 60(2019), 53–65.
  9. On twisted group frames (with C. Cheng),  Lin. Alg. Appl.,569(2019),  285-310.
  10. Phase retrieval of real-valued functions in Sobolev spaces (with Youfa Li), Acta Math. Sinica ,  34(2018), 1788-1794.  
  11. Joint similarities and parameterizations for Naimark complementary frames (with X. Guo),  J. Math. Anal. Appl.,  462(2018), 148–156.
  12. Dilations of operator-valued measures with bounded p-variations and framings on Banach spaces (with D. Larson and R. Liu) ,  J. Funct. Anal. , 274(2018), 1466-1490
  13. Recovery of Signals from  Unordered Partial Frame Coefficients (with F.  Lv and  W.  Sun),   Appl. Comput. Harm. Anal., 44(2018), 38–58.
  14. Stable Recovery of Signals from Frame Coefficients with Erasures at Unknown Locations (with Fusheng Lv and Wenchang Sun),  Sciences in China — Mathematics,  61(2018), 151–172.
  15.  Phase retrieval from multiple-window short-time Fourier measurements (with Lan Li, Cheng Cheng, Qiyu Sun and Guangming Shi),  IEEE Signal Processing Letters, 24(2017), 372–376.
  16. Frame vector multipliers for finite group representations (with Z. Li),  Lin. Alg. Appl.,519(2017),  191–207.
  17. Time-frequency analysis meets operator algebras,  Acta Math. Sinica A, 60(2017), 3–18.
  18. A note on the density theorem for projective unitary representations,  Proc. Amer. Math. Soc., 145(2017), 1739-1745.
  19. Adaptive Optimal Dual Frames for Signal Reconstruction With Erasures (with Q. Guo, J. Leng etc.)  IEEE Access , 4(2016), 7577–7584.
  20. Continuous framings for Banach spaces (with F. Li and P.  Li),  J. Funct. Anal., 271(4) 2016, 992–1021

2011-2015

  1. Spectrally two-uniform frames for erasures, Oper Matrices,  9(2015), 383–399.
  2. Reconstruction of signals from frame coefficients with erasures at unknown locations (with Wenchang Sun),  IEEE Trans. Information Theory,  60(2014), no. 7, 4013–4025
  3. Dilations for systems of imprmimitivity acting on Banach spaces  (with D. Larson, B. Liu and R. Liu), J. Funct. Anal. , 266(12), 2014, 6914–6937
  4. Dilations of frames, operator valued measures and bounded linear maps (with D. Larson, B. Liu and R. Liu),  Contemp. Math., Amer. Math. Soc .,  626, 2014, 33–54
  5. Operator-Valued Measures, Dilations, and the Theory of Frames (84 pages, with D. Larson, B. Liu and R. Liu),  Memoirs  Amer. Math. Soc.,   Vol. 229, No. 1075 (2014)
  6. Divergence of mock and scrambled Fourier series (with D. Dutkay and Q. Sun),   Trans. Amer. Math. Soc.,  366(2014), 2191–2208
  7. Continuous and Discrete Fourier Frames for Fractal Measures (with  D. Dutkay and E. Weber),   Trans. Amer. Math. Soc., 366(2014), 1213–1235
  8. Discrete Gabor Frames in $\ell^2(\bf{Z}^d)$ (with J. Lopez),  Proc. Amer. Math. Soc., 141 (2013),  3839–3851
  9. Linearly connected sequences and spectrally optimal frames for erasures (with S. Pehlivan and  R. Mohapatra),  J. Funct. Anal. ,  265(2013), 2855–2876
  10. Matrix Fourier multipliers for Parseval multi-wavelet frames (with Z. Li), Appl. Comp. Harm. Anal.,   35(2013), 407–418
  11. On common fundamental domains (with D. Dutkay, Palle Jorgensen and G. Picioroaga), Adv.  Math.,  239(2013), 109–127
  12. Lattice titling and density conditions for subspace Gabor frames (with J-P. Gabardo and Y. Li),  J. Funct. Anal. , 265(2013), 1170–1189
  13. Orthogonal projection decomposition of matrices and construction of fusion frames (with J. Leng),  Adv.  in Comput. Math.,    38(2013), 369-381
  14. Centralizers and Jordan derivations for CSL subalgebras of von Neumann algebras (with P. Li and W. Tang),  J. Operator Theory, 69(2013), 117–133
  15. Probability modelled optimal frames for erasures (with J. Leng and T. Huang), Lin. Alg. Appl.,  438(2013), 4222-4236
  16. Dilation of dual frame pairs in Hilbert C*-modules (with W. Jing , D. Larson, P. Li and  R. Mohapatra),  Results in Math.,  63(2013), 241–250
  17. Iterative approximations of exponential bases on fractal measures (with  D. Dutkay and E. Weber),   Numer. Funct. Anal. Optim in Math.,   33(2012), 928–950
  18. The Correlation numerical range of a matrix and the Connes’ embeding problem (with D. Hadwin), Lin. Alg. Appl.,   436(2012), 3139–3148
  19. Derivations on  algebras of operators in Hilbert C*-modules(with P. Li and W. Tang),  Acta Math. Sinica,  28(2012), 1615–1622
  20. Optimal Dual Frames for Communication Coding with Probabilistic Erasures (with J. Leng and T. Huang), IEEE Trans. Signal Processing, 59 (2011), 5380–5389
  21. Operator valued frames and structured quantum channels (with P. Li, B. Meng  and W. Tang), Science in China –Mathematics,  R. Kadison’s 85th birthday special issue. 54(2011), 2361–2372
  22. Optimal dual frames for erasures II (with J. Leng),  Lin. Alg. Appl.,  435 (2011), 1464–1472
  23. Bessel sequences of exponentials on fractal measures (with  D. Dutkay and E. Weber),  J. Funct. Anal. , 261 (2011), 2529–2539
  24. Wavelet frames for (not necessarily reducing) affine subspaces II: The structure of affine subspaces (with Q. Gu), J. Funct. Anal. , 260(2011), 1615–1636
  25. Topological and geometric properties of refinable functions and MRA affine frames (with  Q. Sun and W. Tang)  Appl. Comp. Harm. Anal.,   30(2011), 151–174
  26. Frames and their associated H_F^P-subspaces (with P. Li and W. Tang),  Adv. in Comput. Math.,  34(2011), 185–200
  27. On the Beurling dimension of exponential frames (with D. Dutkay,  Q. Sun and E. Weber),  Adv.  Math.,  226 ( 2011) 285–297
  28. Frames for group representations: A dulaity principle and Feichtingher’s frame conjecture, Mathematisches Forschungsinstitut, Oberwolfach Reports No. 17(2011), 969–972.

2006-2010

  1. Optimal dual frames for erasures (with Jerry Lopez),  Lin. Alg. Appl.,  432 (2010) 471–482
  2. Constructing super Gabor frames: The rational lattice case (with Z. Li), Science in China — A: Mathematics,   53(2010),  3179–3186
  3. Orthogonal exponentials, translations, and Bohr completions (with D. Dutkay and Palle Jorgensen ), J. Funct. Anal. ,  257 (2009), 2999–3019
  4. Sampling expansions in reproducing kernel Hilbert and Banach spaces (with Z. Nashed and Q. Sun),  Numer. Funct. Anal. Optim., 30(2009), 971–987
  5. A duality principle for groups ( with D. Dutkay and  D. Larson),   J. Funct. Anal. ,  257, No.4 ( 2009), 1133–1143
  6. Wavelet Frames for (not necessarily reducing) Affine Subspaces (with Q. Gu),  Appl. Comp. Harm. Anal.,    27(2009),  47–54
  7. On the orthogonality of frames and the density and connectivity  of wavelet frames  (with  D. Larson),  Acta Appl. Math.,  107(2009), 211–222
  8. Perturbation of frames and Riesz bases in Hilbert C*-modules (with  W. Jing  and  R. Mohapatra),  Lin. Alg. Appl.,  431 (2009) 746–759
  9. On the spectra of a Cantor measure (with D. Dutkay, Q. Sun),   Adv.  Math.,   221, No.1 (2009), 251–276
  10. Dilations and completions for Gabor systems,  J.  Fourier Anal. Appl.,  15, No.2 (2009),  201–217
  11. Frames for ICC groups (with D. Dutkay, G. Picioroaga),   J. Funct. Anal.,  256, No. 9 (2009), 3071–3090
  12. The existence of tight Gabor duals for Gabor frames and subspace Gabor frames, J. Funct. Anal.,  256, No. 1(2009), 129–148
  13. Frame duality properties for projective unitary representations (with D. Larson),  Bull. London Math. Soc.,   40(2008), 685–695
  14. Orthonormal dilations of Parseval wavelets (with D. Dutkay, G. Picioroaga, Q. Sun),   Math.  Ann.,  341(2008), 483–515
  15. Riesz bases and their dual modular frames in Hilbert  C*-modules (with  W. Jing , D. Larson and  R. Mohapatra),  J. Math. Anal. Appl.,   343(2008), 246–256
  16. When a characteristic function generates a Gabor frame (with Q. Gu),   Appl. Comp. Harm. Anal.,  24(2008), 190–309
  17. Frame representations and Parseval duals with applications to Gabor frames, Trans. Amer. Math. Soc.,  360(2008), 3307–3326
  18. Refining Algorithms in Correlation Filter Design for Target Detection (with X.  Li, R. Mohapatra, M. Michalak, Z. Nashed), Image and Signal Processing, 2008 CISP ’08. Volume: 1, page(s): 231-238
  19. Classification of finite group frames and super-frames,   Canadian Math. Bull.,   50(2007), 85–96.
  20. Separating vectors for operators (with D. Larson, Z. Pan and W. Wogen),   Proc. Amer. Math. Soc., 135(2007), 713–723.
  21. Structured Parseval frames in Hilbert C*-modules (with J. Wu and R. Mohapatra),   Contemp. Math., Amer. Math. Soc .,   414 (2006), 275–288.

2001-2005

  1. Super-wavelets and decomposable wavelet frames (with Q. Gu), J.  Fourier Anal. Appl.,   11(2005), 683–696.
  2. Sampling expansions for functions having values in a Banach space (with  Ahmed Zayed),   Proc. Amer. Math. Soc., 133(2005), 3597–3607 
  3. Frames, modular functions for shift-invariant subspaces and FMRA wavelet frames (with Q. Gu),  Proc. Amer. Math. Soc.,  133(2005),   815–825
  4. Extensions of  operators (with D. Larson, Z. Pan and W. Wogen),   Indiana  Univ.  J.  Math.,  53(2004),   1151–1169
  5. Balian-Low  phenomenon for subspace Gabor frames (with J-P. Gabardo ) ,  J. Math. Phys.,  45(2004), 3362–3378.
  6. Tight frame approximation  for multi-frames and super-frames,  J. Approx. Theory,   129(2004), 78–93
  7. The uniqueness of the dual of Weyl-Heisenberg subspace frames (with J-P. Gabardo),  Appl. Comp. Harm. Anal.,  17(2004), 226–240 .
  8. The existence of Gabor bases (with Y. Wang),  Contemp. Math.,  345 (2004), 183–192.
  9. The s-elementary wavelets are path-connected (with X. Dai, Y. Diao and Q. Gu),    Proc. Amer. Math. Soc., 132(2004), 2567–2575
  10. Constrained Quadratic Correlation Filters for Target Detection (with R. Muise, A. Mahalanobis, R. Mohapatra, X.  Li and W.  Mikhael),  Applied Optics,  43(2004), 304-314.
  11. Approximations for Gabor and wavelet frames,  Trans. Amer. Math. Soc.,    355 (2003), 3329—3342
  12. Frame representations for group-like unitary operator systems (with J-P. Gabardo ),  J. Operator Theory ,  49 (2003), 223—244
  13. Functional Gabor frame multipliers (with Q. Gu),  J. Geometric Analysis,   13 (2003), 467–478.
  14. The Existence of Subspace Wavelet Sets (with X. Dai, Y. Diao and Q. Gu),   J.  Comp. Appl. Math.,  115 (2003), 83–90
  15. Frames associated with measurable spaces (with J-P. Gabardo ),  Adv.  in Comput. Math., 18 (2003), 127-147
  16. Wavelets with frame multiresolution analysis (with X. Dai, Y. Diao and Q. Gu),    J.  Fourier Anal.  Appl.,  9(2003), 39-48.
  17. Frame Wavelet Sets in R^{d}  (with X. Dai, Y. Diao and Q. Gu),   J.  Comp. Appl. Math.,    115 (2003), 69–82.
  18. The Balian-Low theorem for symplectic lattices in higher dimensions (with K. Grochenig,  C. Heil and G. Kutyniok),  Appl. Comp. Harm. Anal.,13 (2002), 169-176..
  19. Phases for dyadic orthonormal wavelets, (with Q. Gu),     J. Math.  Phys.,   43 (2002), no. 5, 2690–2706.
  20. Frame wavelets in subspaces of R^{d}(with X. Dai, Y. Diao and Q. Gu),     Proc. Amer. Math. Soc., 130 (2002),  3259—3267
  21. Interpolation operators associated with sub-frame sets,    Proc. Amer. Math. Soc., 131 (2002), 275—284
  22. Wandering vector multipliers for unitary groups (with D. Larson),  Trans. Amer. Math. Soc.,   353(2001)3347-3370.
  23. Lattice tiling and Weyl-Heisenberg frames (with W. Yang),    Geometric and Functional Analysis (known as GAFA),  11(2001), 742-758.
  24. Subspace Weyl-Heisenberg frames (with J-P. Gabardo ),  J. Fourier Anal.  Appl., 7(2001), 419-433.
  25. Tight frame approximations for wavelets and Gabor frames,  Wavelet Applications in Singnal and Image Analysis,    Proc.SPIE.,   4478 (2001)135-141.
  26. Phases for orthogonal wavelets, SAMPTA (2001), 81-83

1996-2000

  1. Frames, bases and group representations (with D. Larson),    Memoirs  Amer. Math. Soc.,   697(2000)
  2. On multiresolution analysis wavelets in $R^{n}$ (with Q. Gu),   J. Fourier Anal.  Appl.,  6(2000), 437-448
  3. Gabor frames and operator algebras (withJ-P. Gabardo and D. Larson),  Wavelet Applications in Singnal and Image Analysis,    Proc. SPIE., 4119 (2000), 337-345
  4. Multiresolution analysis of abstract Hilbert spaces and wandering subspaces (with D. Larson, M. Papadakis and T.  Stavropoulos),  Contemp. Math., Amer. Math. Soc.,  247(1999), 259-284.
  5. Frames in Banach spaces (with P. Casazza and D. Larson),  Contemp. Math., Amer. Math. Soc .,   247 (1999) 149-182.
  6. Wandering vectors for irrational rotation unitary systems,   Trans. Amer. Math. Soc.,, 350(1998), 309-320.
  7. Basic properties of wavelets,  J.  Fourier Anal.  Appl., (Wutam Consortium), 4(1998)575-594.
  8. Derivations and isomorphisms of certain reflexive operator algebras (with C. Hou),  Acta Math. Sinica (N. S.),   14 (1998),  105–112.
  9. Additive derivations of certain operator algebras, Acta Math. Sinica (Chinese),   39 (1996),  275–279
  10. Continuity and linearity of additive derivations of nest algebras on Banach spaces.  Chinese Ann. Math. Ser. B 17 (1996), 227–236

Publications before 1996 (also see  MathSciNet)

  1. On some ideals of nest algebras (with C. Hou), Proc. Amer. Math. Soc., 123, no.11(1995), 3449-3453.
  2. Local derivations of nest algebras (with S. Wei), Proc. Amer. Math. Soc.,  no.10(1995), 3095-3100.
  3. On M-ideals and best approximation,  Acta Math. Appl. Sinica(English Ser.)} 10, no.2(1994), 213-219.
  4. Spectrum of the products of operators and compact perturbations (with W. Gong), Proc. Amer. Math. Soc., 120, no.3(1994),755-760.
  5. Additive derivations of certain nest algebras.  Bull. Inst. Math. Acad. Sinica, 22 (1994), 101–112.
  6. On some properties of semi-nest algebras,  Houston J. Math.19,  no.1 (1993), 17-25.
  7. Additive derivations of nest algebras, Proc. Amer. Math. Soc., 119, no.4(1993), 1165-1169.
  8. The first cohomology groups of nest algebras on normed spaces, Proc. Amer. Math. Soc., 118, no.4(1993), 1147- 1149.
  9. Bimodules and cohomology spaces of reflexive operator algebras, Chinese Ann. Math.,  Ser A. 14 (1993), 642–646.
  10. A spectral characterization of rank one normal operators and essentially normal compact operators, Northeast. Math. J.,9 (1993), 461–464.
  11. A note on the commutants of CSL algebras modulo bimodules, Proc. Amer. Math. Soc. 116, no.3(1992), 707-709.
  12. Rank one operators and bimodules of reflexive operator algebras in Banach spaces,  J. Math. Anal. Appl., 161,no.1(1991), 188-193.
  13. On a spectral characterization of rank one matrices (with B.V. Limaye), Linear Algebra Appl., 143 (1991), 1–6.
  14. On isomorphisms and hyper­reflexivity of closed subspace lattices,  Internat.  J.  Math. &  Math.  Sci.,  14, no.3(1991), 447-450
  15. On reflexivity and hyperreflexivity for linear subspace of operators, Chinese Ann. Math. Ser. B, 12, no.1(1991), 40-44.
  16.  A note on a problem of Nordgren, Chinese Quarterly Journal of Mathematics, 6 (1991), 52–54.
  17. Hyper-reflexivity of von Neumann algebras and their latices, Chinese Science Bulletin, 36(19) ( 1991), 1515.
  18. On reflexivity and hyper-reflexivity of matrix operator algebras,  J. of Math., 11 (1991), 119 —?
  19. Best approximations in tensor product spaces ,  Acta Math. Appl. Sinica, 13, no.3(1990), 292-295.
  20. Bimodules of reflexive operator algebras II,  Acta Math Sinica, 33, no.3(1990), 348-352.
  21. On A-submodules for reflexive operator algebras, Proc. Amer. Math. Soc.104, no.4(1988), 1067-1070
  22. On the duality of operator algebras,  Chinese Science Bulletin 33(7) ( 1988), 556.
  23. A note on reflexive Banach spaces, J. Qufu Normal University, 20 (1994), 107 — 108
  24. Grothendieck’s theorem for bilinear functionals on C*-algebras, JQNU, 19 (1993), 23–29
  25. Finite co-dimensional ideals in function algebras, JQNU, 19 (1993), 8–15
  26. A class of special completely positive multi-linear operators, JQNU 18 (1992), no. 3, 7–1
  27. Finite co-dimensional ideals in Banach algebras, JQNU,17 (1991), no. 4, 1–4.
  28. Rank-one operators in strongly reflexive operator algebras, JQNU, 17 (1991), no. 1, 30–33
  29. Some results on dual operator algebras, JQNU,  14(1988), no. 4, 6–12
  30. A best approximation theorem and spaces of quasitriangular operators, JQNU 13 (1987), no. 4, 144–147.
  31. An elementary property of index functions in Banach algebras, JQNU,  13 (1987), no. 3, 199–200.
  32. A topological result on Banach operator spaces and a distance formula (with L. Ge),  JQNU,  13 (1987), no. 1, 31–33
  33. The Putnam-Fuglede theorem, JQNU, 15 (1989), no. 4, 33–34
  34. A note on a generalized moment problem (with J. Zhou), JQNU,  12(1986), no. 1, 25–26
  35. A note on the second mean value theorem for integrations (with X. Jia, This is a publication based on my undergraduate research thesis), JQNU. No. 2 (1981).

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