{"id":16,"date":"2018-01-03T13:50:39","date_gmt":"2018-01-03T18:50:39","guid":{"rendered":"https:\/\/sciences.ucf.edu\/math\/han\/?page_id=16"},"modified":"2025-11-21T14:24:57","modified_gmt":"2025-11-21T19:24:57","slug":"selected-publications","status":"publish","type":"page","link":"https:\/\/sciences.ucf.edu\/math\/han\/selected-publications\/","title":{"rendered":"Selected Publications"},"content":{"rendered":"
    \n
  1. Operator-Valued Measures, Dilations, and the Theory of Frames (84 pages, with D. Larson, B. Liu and R. Liu),\u00a0Memoirs\u00a0 Amer. Math. Soc<\/u><\/em><\/b><\/a>.,\u00a0\u00a0<\/b>\u00a0Vol. 229, No.\u00a0 1075 (2014).<\/li>\n
  2. Frames, bases and group representations (94 pages, with D. Larson), \u00a0\u00a0\u00a0Memoirs\u00a0 Amer. Math. Soc<\/u><\/em><\/b><\/a>.,\u00a0<\/b>\u00a0 697(2000).<\/li>\n
  3. Dilations for operator-valued quantum measures (with Q. Hu, A. Larson and R. Liu), Adv. Math<\/a><\/strong><\/em>., 438(2024), 109476.<\/li>\n
  4. On common fundamental domains (with D. Dutkay, P. Jorgensen and G. Picioroaga),\u00a0Adv. Math.<\/i><\/b><\/a>,\u00a0\u00a0239(2013), 109–127<\/li>\n
  5. On the Beurling dimension of exponential frames (with\u00a0 D. Dutkay,\u00a0 Q. Sun and\u00a0E. Weber),\u00a0\u00a0Adv.\u00a0 Math.<\/i><\/b><\/a>,\u00a0 226 ( 2011) 285–297<\/li>\n
  6. On the spectra of a Cantor measure (with D. Dutkay,\u00a0Q. Sun),\u00a0\u00a0\u00a0Adv.\u00a0 Math.<\/i><\/b><\/a>, \u00a0 221, No.1 (2009), 251–276\u00a0<\/b><\/li>\n
  7. Lattice tiling and\u00a0Weyl-Heisenberg frames (with W. Yang), \u00a0\u00a0\u00a0<\/b>Geometric and Functional Analysis (known as GAFA)<\/u><\/em><\/b>,<\/u><\/b><\/a>\u00a0 11(2001), 742-758.<\/li>\n
  8. Orthonormal dilations of Parseval wavelets (with\u00a0D. Dutkay, G. Picioroaga, Q. Sun), \u00a0\u00a0Math.\u00a0 Ann.,\u00a0\u00a0<\/i><\/b><\/a>341(2008), 483–515<\/li>\n
  9. Continuous and Discrete Fourier Frames for Fractal Measures (with D. Dutkay and E. Weber),\u00a0\u00a0\u00a0Trans<\/u><\/em><\/b><\/a>. Amer. Math. Soc.,<\/u><\/b><\/a><\/em>\u00a0366(2014), 1213–1235<\/li>\n
  10. Divergence of the mock and scrambled Fourier series on fractal measures (with D. Dutkay and Q. Sun),\u00a0\u00a0\u00a0Trans<\/u><\/em><\/b><\/a>. Amer. Math. Soc.,<\/u><\/b><\/a><\/em>\u00a0\u00a0366(2014), 2191–2208<\/li>\n
  11. Frame representations and Parseval duals with applications to Gabor frames,\u00a0Trans<\/u><\/em><\/b><\/a>. Amer. Math. Soc.,<\/u><\/b><\/a><\/em>\u00a0\u00a0<\/em>360(2008), 3307–3326<\/li>\n
  12. Approximations for\u00a0Gabor\u00a0and wavelet frames,\u00a0\u00a0Trans<\/u><\/em><\/b><\/a>. Amer. Math. Soc.,<\/u><\/b><\/a><\/em>\u00a0\u00a0<\/b>355 (2003), 3329\u20143342<\/li>\n
  13. Wandering vector multipliers for unitary groups (with D. Larson),\u00a0\u00a0Trans<\/u><\/em><\/b><\/a>. Amer. Math. Soc.,<\/u><\/b><\/a>\u00a0<\/b>\u00a0 353(2001)3347-3370<\/em>.<\/li>\n
  14. Wandering vectors for irrational rotation unitary systems, \u00a0Trans<\/u><\/em><\/b><\/a>. Amer. Math. Soc.,<\/u><\/b><\/a><\/em>,<\/b> 350(1998), 309-320<\/li>\n
  15. A note on the density theorem for projective unitary representations,\u00a0\u00a0Proc. Amer. Math. Soc<\/a><\/strong><\/em>., 145(2017), 1739-1745<\/li>\n
  16. Discrete Gabor Frames in $\\ell^2(\\bf{Z}^d)$ (with J. Lopez),\u00a0\u00a0Proc<\/u><\/em><\/b>. Amer. Math. Soc.<\/u><\/em><\/b><\/a>,<\/b>\u00a0141 (2013),\u00a0 3839\u20133851<\/li>\n
  17. Separating vectors for operators (with\u00a0D. Larson<\/a>,\u00a0Z. Pan<\/a>\u00a0and\u00a0W. Wogen<\/a>),\u00a0\u00a0\u00a0Proc<\/u><\/em><\/b>. Amer. Math. Soc.<\/u><\/em><\/b><\/a>,<\/b>\u00a0135(2007), 713\u2013723.<\/li>\n
  18. Sampling expansions for functions having values in a Banach space (with\u00a0\u00a0Ahmed Zayed<\/a>),\u00a0\u00a0\u00a0Proc<\/u><\/em><\/b>. Amer. Math. Soc.<\/u><\/em><\/b><\/a>,<\/b>\u00a0133(2005), 3597\u20133607\u00a0<\/b><\/li>\n
  19. Frames, modular functions for shift-invariant subspaces and FMRA wavelet\u00a0frames (with\u00a0Q. Gu<\/a>),\u00a0\u00a0Proc<\/u><\/em><\/b>. Amer. Math. Soc.<\/u><\/em><\/b><\/a>,<\/b>\u00a0 133(2005),\u00a0\u00a0 815\u2013825<\/li>\n
  20. The s-elementary wavelets are path-connected (with\u00a0X. Dai<\/a>,\u00a0Y.\u00a0Diao<\/a>\u00a0and\u00a0Q. Gu<\/a>),\u00a0\u00a0\u00a0\u00a0Proc<\/u><\/em><\/b>. Amer. Math. Soc.<\/u><\/em><\/b><\/a>,<\/b>\u00a0<\/b>132(2004), 2567\u20132575<\/li>\n
  21. Frame wavelets in subspaces of R^{d}(with\u00a0X. Dai<\/a>,\u00a0Y.\u00a0Diao<\/a>\u00a0and\u00a0Q. Gu<\/a>), \u00a0\u00a0\u00a0\u00a0Proc<\/u><\/em><\/b>. Amer. Math. Soc.<\/u><\/em><\/b><\/a>,<\/b>\u00a0130 (2002),\u00a0 3259\u20143267<\/li>\n
  22. Interpolation operators associated with sub-frame sets, \u00a0\u00a0\u00a0Proc<\/u><\/em><\/b>. Amer. Math. Soc.<\/u><\/em><\/b><\/a>,<\/b>\u00a0131 (2002), 275\u2014284<\/li>\n
  23. On some ideals of nest algebras (with C. Hou),\u00a0Proc. Amer. Math. Soc.,<\/a><\/strong><\/em>\u00a0123, no.11(1995), 3449-3453.<\/li>\n
  24. Local derivations of nest algebras (with S. Wei),\u00a0Proc. Amer. Math. Soc.<\/a>,\u00a0<\/strong><\/em>\u00a0no.10(1995), 3095-3100.<\/li>\n
  25. Spectrum of the products of operators and compact perturbations (with W. Gong),\u00a0Proc. Amer. Math. Soc.,<\/a><\/strong><\/em>\u00a0120, no.3(1994),755-760<\/li>\n
  26. Additive derivations of nest algebras,\u00a0Proc. Amer. Math. Soc.,<\/a><\/strong><\/em>\u00a0<\/span>119, no.4(1993), 1165-1169.<\/li>\n
  27. The first cohomology groups of nest algebras on normed spaces,\u00a0Proc. Amer. Math. Soc.,<\/a><\/strong><\/em>\u00a0118, no.4(1993), 1147- 1149.<\/li>\n
  28. A note on the commutants of CSL algebras modulo bimodules,\u00a0Proc. Amer. Math. Soc.<\/a><\/strong><\/em>\u00a0116, no.3(1992), 707-709<\/li>\n
  29. Frame duality properties for projective unitary representations (with\u00a0D. Larson),\u00a0\u00a0Bull. London Math. Soc.,<\/a><\/i><\/b>\u00a0\u00a0 40(2008), 685\u2013695<\/li>\n
  30. Extensions of\u00a0\u00a0operators (with\u00a0D. Larson,\u00a0Z. Pan\u00a0and\u00a0W. Wogen), \u00a0\u00a0<\/a>Indiana\u00a0 Univ.\u00a0 J.\u00a0 Math.<\/a>,<\/u><\/em><\/b>\u00a0 53(2004),\u00a0\u00a0 1151\u20131169<\/li>\n
  31. Determination of compactly supported functions in shift-invariant space by single-angle Radon samples (with S. Fan and Y. Li), \u00a0J. Funct. Anal.<\/a>,\u00a0<\/strong><\/em> 285(2023), 110151<\/li>\n
  32. Gabor single-frame and multi-frame multipliers in any given dimension (with\u00a0Y. Diao\u00a0and Z. Li),\u00a0\u00a0J. Funct. Anal.<\/i><\/b><\/a>\u00a0<\/a>,\u00a0\u00a0 280(2021), 108960<\/span><\/a><\/li>\n
  33. Dilations of operator-valued measures with bounded p-variations and framings on Banach spaces (with D. Larson and R. Liu) , J. Fu<\/strong>nct. Anal.,<\/em><\/strong><\/a> 274(2018), 1466 –1490<\/li>\n
  34. Continuous framings for Banach spaces (with F. Li and P.\u00a0 Li),\u00a0\u00a0J. Funct. Anal<\/a><\/em><\/strong>., 271(4) 2016, 992–1021<\/li>\n
  35. Dilations for systems of imprmimitivity acting on Banach spaces\u00a0(with Larson, B. Liu and R. Liu),\u00a0J. Funct. Anal.<\/i><\/b><\/a>\u00a0<\/a>,\u00a0266(12), 2014, 6914–6937<\/li>\n
  36. Linearly connected sequences and spectrally optimal frames for erasures (with S. Pehlivan and R. Mohapatra),\u00a0\u00a0J. Funct. Anal.<\/i><\/b><\/a>\u00a0<\/a>,\u00a0 265(2013), 2855–2876<\/li>\n
  37. Lattice titling and density conditions for subspace Gabor frames (with J-P. Gabardo and Y. Li),\u00a0\u00a0J. Funct. Anal.<\/i><\/b><\/a>\u00a0<\/a>,\u00a0265(2013), 1170–1189<\/li>\n
  38. Bessel sequences of exponentials on fractal measures (with\u00a0\u00a0D. Dutkay\u00a0and\u00a0E. Weber),\u00a0\u00a0J. Funct. Anal.<\/i><\/b><\/a>\u00a0<\/a>,\u00a0261 (2011), 2529–2539<\/li>\n
  39. Wavelet frames for (not necessarily reducing) affine subspaces II: The structure of affine subspaces (with\u00a0Q. Gu),\u00a0J. Funct. Anal.<\/i><\/b><\/a>\u00a0<\/a>,\u00a0260(2011), 1615–1636<\/li>\n
  40. Orthogonal exponentials, translations, and Bohr completions (with D. Dutkay and Palle Jorgensen ),\u00a0J. Funct. Anal.<\/i><\/b><\/a>\u00a0<\/a>,\u00a0\u00a0257 (2009), 2999–3019<\/li>\n
  41. A duality principle for groups ( with D. Dutkay and\u00a0 D. Larson), \u00a0\u00a0J. Funct. Anal.<\/i><\/b><\/a>\u00a0<\/a>,\u00a0\u00a0257, No.4 ( 2009), 1133–1143<\/li>\n
  42. Frames for ICC groups (with D. Dutkay, G. Picioroaga),\u00a0\u00a0\u00a0J. Funct. Anal.<\/i><\/b><\/a>,\u00a0\u00a0256, No. 9 (2009), 3071–3090<\/li>\n
  43. The existence of tight Gabor duals for Gabor frames and subspace Gabor frames,\u00a0J. Funct. Anal.<\/i><\/b><\/a>,\u00a0 256, No. 1(2009), 129–148<\/li>\n
  44. Dynamical frames and hyperinvariant subspaces (with V. Bailey, K. Kornelson, D. Larson and R. Liu),\u00a0 Appl. Comput. Harm. Anal<\/a><\/strong><\/em>., 81, Feb. 2026<\/li>\n
  45. FROG-measurement based phase retrieval for analytic signals (with Y. Li and Y. Ma), <\/a><\/span>Appl. Comput. Harm. Anal<\/a><\/strong><\/em>., 55(2021), 199-222<\/li>\n
  46. Erasure recovery matrices for encoder (with D. Larson, S. Scholze and W. Sun),\u00a0Appl. Comput. Harm. Anal<\/i><\/a>.<\/strong>, 48(2020), 766-786<\/li>\n
  47. Recovery of Signals from Unordered Partial Frame Coefficients (with F. Lv and W. Sun), Appl. Comput. Harm. Anal.<\/a><\/em><\/strong>, 44(2018), 38\u201358<\/li>\n
  48. Matrix Fourier multipliers for Parseval multi-wavelet frames (with Z. Li),\u00a0Appl. Comp. Harm. Anal.,<\/u><\/em><\/b><\/a>\u00a0<\/b>\u00a0 35(2013), 407–418<\/li>\n
  49. Topological and geometric properties of refinable functions and MRA affine frames (with\u00a0\u00a0Q. Sun and W. Tang)\u00a0\u00a0Appl. Comp. Harm. Anal.,<\/u><\/em><\/b><\/a>\u00a0<\/b>\u00a0 30(2011), 151–174<\/li>\n
  50. Wavelet Frames for (not necessarily reducing) Affine Subspaces (with Q. Gu),\u00a0\u00a0Appl. Comp. Harm. Anal.,<\/u><\/em><\/b><\/a>\u00a0<\/b>\u00a0\u00a0 27(2009),\u00a0 47–54<\/li>\n
  51. When a characteristic function generates a Gabor frame (with Q. Gu),\u00a0\u00a0\u00a0Appl. Comp. Harm. Anal.,<\/u><\/em><\/b><\/a>\u00a0\u00a0<\/b>24(2008), 190–309<\/li>\n
  52. The uniqueness of the dual of\u00a0Weyl-Heisenberg subspace frames (with J-P.\u00a0Gabardo)),\u00a0\u00a0Appl. Comp. Harm. Anal.,<\/u><\/em><\/b><\/a>\u00a0 17(2004), 226–240 .<\/li>\n
  53. The\u00a0Balian-Low theorem for\u00a0symplectic\u00a0lattices in higher dimensions (with K.\u00a0Grochenig,\u00a0 C.\u00a0Heil\u00a0and G.\u00a0Kutyniok),\u00a0\u00a0Appl. Comp. Harm. Anal.,<\/u><\/em><\/b><\/a>13 (2002), 169-176.<\/li>\n
  54. The density theorem for operator-valued frames via square-integrable representations of locally compact groups (with P. Li and J. Wang),\u00a0 Journal of Fourier Anal. App<\/a>l<\/strong><\/em>.,\u00a02024, available online<\/li>\n
  55. A duality principle for groups II: Multi-frames meet super-frames<\/span>\u00a0 (with <\/a>R Balan, D Dutkay, D D Larson, F Luef),\u00a0 Journal of Fourier Anal. App<\/a>l<\/strong><\/em>.,\u00a0 \u00a026 (6) (2020), 1-19.<\/li>\n
  56. Frame phase-retrievability and exact phase-retrieval frames (with T. Juste. Y. Liu and W. Sun),\u00a0 J<\/u><\/em><\/b><\/a>. Fourier\u00a0Anal.\u00a0Appl.<\/i><\/u><\/b><\/a>, <\/b>25(2019), 3154–3173<\/li>\n
  57. Phase retrievable projective representation frames for finite abelian groups (with J. Brennan, C. Cheng, T. Juste \u00a0and L. Li), \u00a0J<\/u><\/em><\/b><\/a>. Fourier\u00a0Anal.\u00a0Appl.<\/i><\/u><\/b><\/a>,\u00a0<\/b>\u00a025(2019), 86-100.<\/li>\n
  58. Dilations and completions for Gabor systems,\u00a0\u00a0J<\/u><\/em><\/b><\/a>.\u00a0 Fourier\u00a0Anal.\u00a0Appl.<\/u><\/em><\/b><\/a>,\u00a0\u00a0<\/b>15\u00a0(2009),\u00a0 201–217<\/li>\n
  59. Super-wavelets and decomposable wavelet frames (with Q. Gu),\u00a0\u00a0J<\/u><\/em><\/b><\/a>.\u00a0 Fourier\u00a0Anal.\u00a0Appl.<\/u><\/em><\/b><\/a>,<\/b>\u00a0\u00a0 11(2005), 683–696<\/li>\n
  60. Wavelets with frame\u00a0multiresolution\u00a0analysis (with X. Dai, Y. Diao and Q. Gu) \u00a0\u00a0J.\u00a0 Fourier Anal.\u00a0 Appl.<\/u><\/em><\/b><\/a>,<\/b>\u00a0 9(2003), 39-48<\/li>\n
  61. Subspace\u00a0Weyl-Heisenberg frames (with J-P Gabardo),\u00a0\u00a0J<\/u><\/em><\/b><\/a>. Fourier Anal.\u00a0 Appl.<\/u><\/em><\/b><\/a>,\u00a0<\/u><\/b>7(2001), 419-433.<\/li>\n
  62. On\u00a0multiresolution\u00a0analysis wavelets in R^n (with Q. Gu), \u00a0\u00a0J. Fourier Anal.\u00a0 Appl.<\/em><\/a><\/u><\/b>,<\/b>\u00a0 247 (1999) 149-182.<\/li>\n
  63. Basic properties of wavelets,\u00a0\u00a0<\/b>J<\/u><\/em><\/b><\/a>.\u00a0 Fourier\u00a0Anal.\u00a0 Appl.<\/u><\/em><\/b><\/a>,<\/b>\u00a0(a member of Wutam\u00a0Consortium), 4(1998)575-59<\/li>\n
  64. Reconstruction of signals from frame coefficients with erasures at unknown locations (with\u00a0Wenchang Sun),\u00a0\u00a0IEEE Trans. Information Theory,<\/u><\/em><\/b><\/a>\u00a0 60(2014), no. 7, 4013–4025<\/li>\n
  65. Optimal Dual Frames for Communication Coding with Probabilistic Erasures (with J. Leng and T. Huang),\u00a0IEEE Trans. Signal Processing<\/a><\/i><\/b>, 59 (2011), 5380–5389<\/li>\n
  66. \u00a0Phase retrieval from multiple-window short-time Fourier measurements (with Lan Li, Cheng Cheng, Qiyu Sun and Guangming Shi),\u00a0\u00a0IEEE Signal Processing Letters<\/a><\/strong><\/em>, 24(2017), 372\u2013376<\/li>\n<\/ol>\n
    \n

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    Operator-Valued Measures, Dilations, and the Theory of Frames (84 pages, with D. Larson, B. Liu and R. Liu),\u00a0Memoirs\u00a0 Amer. Math. Soc.,\u00a0\u00a0\u00a0Vol. 229, No.\u00a0 1075 (2014). Frames, bases and group representations (94 pages, with D. Larson), \u00a0\u00a0\u00a0Memoirs\u00a0 Amer. Math. Soc.,\u00a0\u00a0 697(2000). Dilations for operator-valued quantum measures (with Q. Hu, A. Larson and R. Liu), Adv. Math., […]<\/p>\n","protected":false},"author":3,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-16","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sciences.ucf.edu\/math\/han\/wp-json\/wp\/v2\/pages\/16","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sciences.ucf.edu\/math\/han\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sciences.ucf.edu\/math\/han\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sciences.ucf.edu\/math\/han\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/sciences.ucf.edu\/math\/han\/wp-json\/wp\/v2\/comments?post=16"}],"version-history":[{"count":11,"href":"https:\/\/sciences.ucf.edu\/math\/han\/wp-json\/wp\/v2\/pages\/16\/revisions"}],"predecessor-version":[{"id":528,"href":"https:\/\/sciences.ucf.edu\/math\/han\/wp-json\/wp\/v2\/pages\/16\/revisions\/528"}],"wp:attachment":[{"href":"https:\/\/sciences.ucf.edu\/math\/han\/wp-json\/wp\/v2\/media?parent=16"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}