Recent Acknowledgements:
- Frames, bases and group representations (with D. Larson), Memoirs Amer. Math. Soc., 697(2000)
- Operator-Valued Measures, Dilations, and the Theory of Frames (with D. Larson, B. Liu and R. Liu), Memoirs Amer. Math. Soc., 1075 (2014)
- Frames for Undergraduates (co-authored with D. Larson, K. Kornelson and E. Weber),
Mathematical Library Book Series, Amer. Math. Soc., (2007), 295 pp., Softcover, ISBN-10: 0-8218-4212-9, ISBN-13: 978-0-8218-4212-6 - Operator Theory, Operator Algebras, and Applications (co-edited with Palle Jorgensen, David Larson),
American Mathematical Society, Contemporary Mathematics, Vol. 414, 2006 - Aspects of Gabor analysis and operator algebras (co-authored with J-P. Gabardo), one chapter in
Advances in Gabor Analysis , Eds. H. G. Feichtinger and T. Strohmer, Birkh\”{a}user,(2002), 129–150. - Applied Harmonic Analysis: Wavelets and Sampling (co-edited with D. Dutkay, P. Jorgensen and Q. Sun), Acta Appl. Math., Vol. 107(N0. 1, 2, 3), 2009
- Unitary Systems and Bessel Generator Multipliers (with David Larson), Chapter 7 in Wavelets and Multiscale Analysis–Theory and Applications, Springer, 2011
Research papers
2021-2025
- Zero-error correctibility and phase retrievability for twirling channels (with Kai Liu), Reports on Mathematical Physics, 93(2024), 87-102.
- Dilations for operator-valued quantum measures (with Q. Hu, A. Larson and R. Liu), Advances in Mathematics., 438(2024), 109476.
- 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
- 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
- Orbit-injective covariant quantum channels (with and C. Cheng and K. Liu), Linear Alg. Appl., 668 (2023), 28–50.
- Generalized Choi-Kraus dilations of linear maps between matrix algebras (with Q. Hu and R. Liu), Oper. Matrices 16 (2022), no. 4, 1219–1237
- 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.
- FROG-measurement based phase retrieval for analytic signals (with Y. Li and Y. Ma), Appl. Comput. Harm. Anal., 55(2021), 199-222
- Gabor single-frame and multi-frame multipliers in any given dimension (with Y. Diao and Z. Li), J. Funct. Anal. , 280(2021), 108960
- Nonuniform sampling and approximation in Sobolev spaces from perturbations of framelet systems (with Y. Li etc). Sciences in China – Mathematics, 64(2021), 351-372
- Injective continuous frames and quantum detections (with Q. Hu, R. Liu), Banach J. Math. Anal., 15 (1) (2021), 1-24
2016-2020
- 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
- Erasure recovery matrices for encoder protection (with D. Larson, S. Scholze and W. Sun), Appl. Comput. Harm. Anal., 48(2020), 766-786
- Structural properties of homomorphism dilation systems (with D. Larson and R. Liu ), Chinese Annals of Mathematics Ser.B, 41(2020), 585-600.
- Frames and Finite-Rank Integral Representations of Positive Operator-Valued Measures (with J-P. Gabardo), Acta Appl. Math.,166(2020), 11-27.
- Frame Phase-Retrievability and Exact Phase-Retrievable Frames (with T. Juste, Y. Li and W. Sun), J. Fourier Anal. Appl., 25(2019), 3154–3173
- Phase-retrievable operator-valued frames and representations of quantum channels (with Ted Juste), Lin. Alg. Appl., 579(2019), 148–168.
- 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.
- Functional matrix multipliers for Parseval Gabor multi-frame generators (with Z. Li), Acta Appl. Math., 60(2019), 53–65.
- On twisted group frames (with C. Cheng), Lin. Alg. Appl.,569(2019), 285-310.
- Phase retrieval of real-valued functions in Sobolev spaces (with Youfa Li), Acta Math. Sinica , 34(2018), 1788-1794.
- Joint similarities and parameterizations for Naimark complementary frames (with X. Guo), J. Math. Anal. Appl., 462(2018), 148–156.
- 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
- Recovery of Signals from Unordered Partial Frame Coefficients (with F. Lv and W. Sun), Appl. Comput. Harm. Anal., 44(2018), 38–58.
- 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.
- 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.
- Frame vector multipliers for finite group representations (with Z. Li), Lin. Alg. Appl.,519(2017), 191–207.
- Time-frequency analysis meets operator algebras, Acta Math. Sinica A, 60(2017), 3–18.
- A note on the density theorem for projective unitary representations, Proc. Amer. Math. Soc., 145(2017), 1739-1745.
- Adaptive Optimal Dual Frames for Signal Reconstruction With Erasures (with Q. Guo, J. Leng etc.) IEEE Access , 4(2016), 7577–7584.
- Continuous framings for Banach spaces (with F. Li and P. Li), J. Funct. Anal., 271(4) 2016, 992–1021
2011-2015
- Spectrally two-uniform frames for erasures, Oper Matrices, 9(2015), 383–399.
- Reconstruction of signals from frame coefficients with erasures at unknown locations (with Wenchang Sun), IEEE Trans. Information Theory, 60(2014), no. 7, 4013–4025
- 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
- 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
- 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)
- Divergence of mock and scrambled Fourier series (with D. Dutkay and Q. Sun), Trans. Amer. Math. Soc., 366(2014), 2191–2208
- Continuous and Discrete Fourier Frames for Fractal Measures (with D. Dutkay and E. Weber), Trans. Amer. Math. Soc., 366(2014), 1213–1235
- Discrete Gabor Frames in $\ell^2(\bf{Z}^d)$ (with J. Lopez), Proc. Amer. Math. Soc., 141 (2013), 3839–3851
- Linearly connected sequences and spectrally optimal frames for erasures (with S. Pehlivan and R. Mohapatra), J. Funct. Anal. , 265(2013), 2855–2876
- Matrix Fourier multipliers for Parseval multi-wavelet frames (with Z. Li), Appl. Comp. Harm. Anal., 35(2013), 407–418
- On common fundamental domains (with D. Dutkay, Palle Jorgensen and G. Picioroaga), Adv. Math., 239(2013), 109–127
- Lattice titling and density conditions for subspace Gabor frames (with J-P. Gabardo and Y. Li), J. Funct. Anal. , 265(2013), 1170–1189
- Orthogonal projection decomposition of matrices and construction of fusion frames (with J. Leng), Adv. in Comput. Math., 38(2013), 369-381
- Centralizers and Jordan derivations for CSL subalgebras of von Neumann algebras (with P. Li and W. Tang), J. Operator Theory, 69(2013), 117–133
- Probability modelled optimal frames for erasures (with J. Leng and T. Huang), Lin. Alg. Appl., 438(2013), 4222-4236
- 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
- Iterative approximations of exponential bases on fractal measures (with D. Dutkay and E. Weber), Numer. Funct. Anal. Optim in Math., 33(2012), 928–950
- The Correlation numerical range of a matrix and the Connes’ embeding problem (with D. Hadwin), Lin. Alg. Appl., 436(2012), 3139–3148
- Derivations on algebras of operators in Hilbert C*-modules(with P. Li and W. Tang), Acta Math. Sinica, 28(2012), 1615–1622
- Optimal Dual Frames for Communication Coding with Probabilistic Erasures (with J. Leng and T. Huang), IEEE Trans. Signal Processing, 59 (2011), 5380–5389
- 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
- Optimal dual frames for erasures II (with J. Leng), Lin. Alg. Appl., 435 (2011), 1464–1472
- Bessel sequences of exponentials on fractal measures (with D. Dutkay and E. Weber), J. Funct. Anal. , 261 (2011), 2529–2539
- Wavelet frames for (not necessarily reducing) affine subspaces II: The structure of affine subspaces (with Q. Gu), J. Funct. Anal. , 260(2011), 1615–1636
- 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
- Frames and their associated H_F^P-subspaces (with P. Li and W. Tang), Adv. in Comput. Math., 34(2011), 185–200
- On the Beurling dimension of exponential frames (with D. Dutkay, Q. Sun and E. Weber), Adv. Math., 226 ( 2011) 285–297
- Frames for group representations: A dulaity principle and Feichtingher’s frame conjecture, Mathematisches Forschungsinstitut, Oberwolfach Reports No. 17(2011), 969–972.
2006-2010
- Optimal dual frames for erasures (with Jerry Lopez), Lin. Alg. Appl., 432 (2010) 471–482
- Constructing super Gabor frames: The rational lattice case (with Z. Li), Science in China — A: Mathematics, 53(2010), 3179–3186
- Orthogonal exponentials, translations, and Bohr completions (with D. Dutkay and Palle Jorgensen ), J. Funct. Anal. , 257 (2009), 2999–3019
- Sampling expansions in reproducing kernel Hilbert and Banach spaces (with Z. Nashed and Q. Sun), Numer. Funct. Anal. Optim., 30(2009), 971–987
- A duality principle for groups ( with D. Dutkay and D. Larson), J. Funct. Anal. , 257, No.4 ( 2009), 1133–1143
- Wavelet Frames for (not necessarily reducing) Affine Subspaces (with Q. Gu), Appl. Comp. Harm. Anal., 27(2009), 47–54
- On the orthogonality of frames and the density and connectivity of wavelet frames (with D. Larson), Acta Appl. Math., 107(2009), 211–222
- Perturbation of frames and Riesz bases in Hilbert C*-modules (with W. Jing and R. Mohapatra), Lin. Alg. Appl., 431 (2009) 746–759
- On the spectra of a Cantor measure (with D. Dutkay, Q. Sun), Adv. Math., 221, No.1 (2009), 251–276
- Dilations and completions for Gabor systems, J. Fourier Anal. Appl., 15, No.2 (2009), 201–217
- Frames for ICC groups (with D. Dutkay, G. Picioroaga), J. Funct. Anal., 256, No. 9 (2009), 3071–3090
- The existence of tight Gabor duals for Gabor frames and subspace Gabor frames, J. Funct. Anal., 256, No. 1(2009), 129–148
- Frame duality properties for projective unitary representations (with D. Larson), Bull. London Math. Soc., 40(2008), 685–695
- Orthonormal dilations of Parseval wavelets (with D. Dutkay, G. Picioroaga, Q. Sun), Math. Ann., 341(2008), 483–515
- 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
- When a characteristic function generates a Gabor frame (with Q. Gu), Appl. Comp. Harm. Anal., 24(2008), 190–309
- Frame representations and Parseval duals with applications to Gabor frames, Trans. Amer. Math. Soc., 360(2008), 3307–3326
- 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
- Classification of finite group frames and super-frames, Canadian Math. Bull., 50(2007), 85–96.
- Separating vectors for operators (with D. Larson, Z. Pan and W. Wogen), Proc. Amer. Math. Soc., 135(2007), 713–723.
- Structured Parseval frames in Hilbert C*-modules (with J. Wu and R. Mohapatra), Contemp. Math., Amer. Math. Soc ., 414 (2006), 275–288.
2001-2005
- Super-wavelets and decomposable wavelet frames (with Q. Gu), J. Fourier Anal. Appl., 11(2005), 683–696.
- Sampling expansions for functions having values in a Banach space (with Ahmed Zayed), Proc. Amer. Math. Soc., 133(2005), 3597–3607
- Frames, modular functions for shift-invariant subspaces and FMRA wavelet frames (with Q. Gu), Proc. Amer. Math. Soc., 133(2005), 815–825
- Extensions of operators (with D. Larson, Z. Pan and W. Wogen), Indiana Univ. J. Math., 53(2004), 1151–1169
- Balian-Low phenomenon for subspace Gabor frames (with J-P. Gabardo ) , J. Math. Phys., 45(2004), 3362–3378.
- Tight frame approximation for multi-frames and super-frames, J. Approx. Theory, 129(2004), 78–93
- The uniqueness of the dual of Weyl-Heisenberg subspace frames (with J-P. Gabardo), Appl. Comp. Harm. Anal., 17(2004), 226–240 .
- The existence of Gabor bases (with Y. Wang), Contemp. Math., 345 (2004), 183–192.
- The s-elementary wavelets are path-connected (with X. Dai, Y. Diao and Q. Gu), Proc. Amer. Math. Soc., 132(2004), 2567–2575
- 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.
- Approximations for Gabor and wavelet frames, Trans. Amer. Math. Soc., 355 (2003), 3329—3342
- Frame representations for group-like unitary operator systems (with J-P. Gabardo ), J. Operator Theory , 49 (2003), 223—244
- Functional Gabor frame multipliers (with Q. Gu), J. Geometric Analysis, 13 (2003), 467–478.
- The Existence of Subspace Wavelet Sets (with X. Dai, Y. Diao and Q. Gu), J. Comp. Appl. Math., 115 (2003), 83–90
- Frames associated with measurable spaces (with J-P. Gabardo ), Adv. in Comput. Math., 18 (2003), 127-147
- Wavelets with frame multiresolution analysis (with X. Dai, Y. Diao and Q. Gu), J. Fourier Anal. Appl., 9(2003), 39-48.
- Frame Wavelet Sets in R^{d} (with X. Dai, Y. Diao and Q. Gu), J. Comp. Appl. Math., 115 (2003), 69–82.
- 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..
- Phases for dyadic orthonormal wavelets, (with Q. Gu), J. Math. Phys., 43 (2002), no. 5, 2690–2706.
- Frame wavelets in subspaces of R^{d}(with X. Dai, Y. Diao and Q. Gu), Proc. Amer. Math. Soc., 130 (2002), 3259—3267
- Interpolation operators associated with sub-frame sets, Proc. Amer. Math. Soc., 131 (2002), 275—284
- Wandering vector multipliers for unitary groups (with D. Larson), Trans. Amer. Math. Soc., 353(2001)3347-3370.
- Lattice tiling and Weyl-Heisenberg frames (with W. Yang), Geometric and Functional Analysis (known as GAFA), 11(2001), 742-758.
- Subspace Weyl-Heisenberg frames (with J-P. Gabardo ), J. Fourier Anal. Appl., 7(2001), 419-433.
- Tight frame approximations for wavelets and Gabor frames, Wavelet Applications in Singnal and Image Analysis, Proc.SPIE., 4478 (2001)135-141.
- Phases for orthogonal wavelets, SAMPTA (2001), 81-83
1996-2000
- Frames, bases and group representations (with D. Larson), Memoirs Amer. Math. Soc., 697(2000)
- On multiresolution analysis wavelets in $R^{n}$ (with Q. Gu), J. Fourier Anal. Appl., 6(2000), 437-448
- Gabor frames and operator algebras (withJ-P. Gabardo and D. Larson), Wavelet Applications in Singnal and Image Analysis, Proc. SPIE., 4119 (2000), 337-345
- 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.
- Frames in Banach spaces (with P. Casazza and D. Larson), Contemp. Math., Amer. Math. Soc ., 247 (1999) 149-182.
- Wandering vectors for irrational rotation unitary systems, Trans. Amer. Math. Soc.,, 350(1998), 309-320.
- Basic properties of wavelets, J. Fourier Anal. Appl., (Wutam Consortium), 4(1998)575-594.
- Derivations and isomorphisms of certain reflexive operator algebras (with C. Hou), Acta Math. Sinica (N. S.), 14 (1998), 105–112.
- Additive derivations of certain operator algebras, Acta Math. Sinica (Chinese), 39 (1996), 275–279
- 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)
- On some ideals of nest algebras (with C. Hou), Proc. Amer. Math. Soc., 123, no.11(1995), 3449-3453.
- Local derivations of nest algebras (with S. Wei), Proc. Amer. Math. Soc., no.10(1995), 3095-3100.
- On M-ideals and best approximation, Acta Math. Appl. Sinica(English Ser.)} 10, no.2(1994), 213-219.
- Spectrum of the products of operators and compact perturbations (with W. Gong), Proc. Amer. Math. Soc., 120, no.3(1994),755-760.
- Additive derivations of certain nest algebras. Bull. Inst. Math. Acad. Sinica, 22 (1994), 101–112.
- On some properties of semi-nest algebras, Houston J. Math.19, no.1 (1993), 17-25.
- Additive derivations of nest algebras, Proc. Amer. Math. Soc., 119, no.4(1993), 1165-1169.
- The first cohomology groups of nest algebras on normed spaces, Proc. Amer. Math. Soc., 118, no.4(1993), 1147- 1149.
- Bimodules and cohomology spaces of reflexive operator algebras, Chinese Ann. Math., Ser A. 14 (1993), 642–646.
- A spectral characterization of rank one normal operators and essentially normal compact operators, Northeast. Math. J.,9 (1993), 461–464.
- A note on the commutants of CSL algebras modulo bimodules, Proc. Amer. Math. Soc. 116, no.3(1992), 707-709.
- Rank one operators and bimodules of reflexive operator algebras in Banach spaces, J. Math. Anal. Appl., 161,no.1(1991), 188-193.
- On a spectral characterization of rank one matrices (with B.V. Limaye), Linear Algebra Appl., 143 (1991), 1–6.
- On isomorphisms and hyperreflexivity of closed subspace lattices, Internat. J. Math. & Math. Sci., 14, no.3(1991), 447-450
- On reflexivity and hyperreflexivity for linear subspace of operators, Chinese Ann. Math. Ser. B, 12, no.1(1991), 40-44.
- A note on a problem of Nordgren, Chinese Quarterly Journal of Mathematics, 6 (1991), 52–54.
- Hyper-reflexivity of von Neumann algebras and their latices, Chinese Science Bulletin, 36(19) ( 1991), 1515.
- On reflexivity and hyper-reflexivity of matrix operator algebras, J. of Math., 11 (1991), 119 —?
- Best approximations in tensor product spaces , Acta Math. Appl. Sinica, 13, no.3(1990), 292-295.
- Bimodules of reflexive operator algebras II, Acta Math Sinica, 33, no.3(1990), 348-352.
- On A-submodules for reflexive operator algebras, Proc. Amer. Math. Soc.104, no.4(1988), 1067-1070
- On the duality of operator algebras, Chinese Science Bulletin 33(7) ( 1988), 556.
- A note on reflexive Banach spaces, J. Qufu Normal University, 20 (1994), 107 — 108
- Grothendieck’s theorem for bilinear functionals on C*-algebras, JQNU, 19 (1993), 23–29
- Finite co-dimensional ideals in function algebras, JQNU, 19 (1993), 8–15
- A class of special completely positive multi-linear operators, JQNU 18 (1992), no. 3, 7–1
- Finite co-dimensional ideals in Banach algebras, JQNU,17 (1991), no. 4, 1–4.
- Rank-one operators in strongly reflexive operator algebras, JQNU, 17 (1991), no. 1, 30–33
- Some results on dual operator algebras, JQNU, 14(1988), no. 4, 6–12
- A best approximation theorem and spaces of quasitriangular operators, JQNU 13 (1987), no. 4, 144–147.
- An elementary property of index functions in Banach algebras, JQNU, 13 (1987), no. 3, 199–200.
- A topological result on Banach operator spaces and a distance formula (with L. Ge), JQNU, 13 (1987), no. 1, 31–33
- The Putnam-Fuglede theorem, JQNU, 15 (1989), no. 4, 33–34
- A note on a generalized moment problem (with J. Zhou), JQNU, 12(1986), no. 1, 25–26
- 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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