Recent Publications

Book

  • Eds. P. G. Casazza and G. Kutyniok, Finite Frames: Theory and Applications, Birkhäuser, Boston (2012). amazon

2014

  • Y. Lonke, Extensions of pure states and the Laurent operator, M.Sc. Thesis, Hebrew University at Jerusalem - translated from Hebrew to English for the first time. pdf
  • P.G. Casazza, E. Pinkham, B. Tuomanen, Riesz outer product Hilbert space frames: Quantitative bounds, topological properties, and full geometric characterization, (submitted). pdf
  • S. Bahmanpour, J. Cahill, P.G. Casazza, J. Jasper, L.M. Woodland, Phase retrieval and norm retrieval, Contemp. Math. (submitted). pdf
  • M. Caspers, S. Montgomery-Smith, D. Potapov, F. Sukochev, The best constants for operator Lipschitz functions on Schatten classes, J. Four. Anals. (2014). pdf
  • S. Montgomery-Smith, Hamiltonians representing equations of motion with damping due to friction, Electron. J. Diff. Equ. 2014 No. 89 (2014) 1-10. pdf
  • S. Montgomery-Smith, Non-linear instability of periodic orbits of suspensions of thin fibers in fluids, submitted. pdf
  • A. Conca, D. Edidin, M. Hering, C. Vinzant, An algebraic characterization of injectivity in phase retrieval, Appl. Comput. Harmon. Anal. in press (2014). pdf
  • J. C. Tremain, Intelligence, creativity and conformity, To appear: MAA Publication: I, Mathematician. pdf For the extended version see: pdf
  • P.G. Casazza, A brief introduction to Hilbert space frame theory and its applications, submitted. pdf
  • P.G. Casazza, J.C. Tremain, Consequences of the Marcus/Spielman/Srivastava solution of the Kadison-Singer problem, arXiv:1407:4768. pdf
  • B. Bodmann, G. Kutyniok, X. Zhuang, Gabor shearlets, Appl. Comput. Harmon. Anal. in press (2014). pdf
  • S. Li, Y. Liu, T. Mi, Fast thresholding algorithms with feedbacks for sparse signal recovery, Appl. Comput. Harmon. Anal. 37 No. 1 (2014) 69-88. pdf
  • D. Ellis, E. Hayashi, S. Li, Tight and full spark Chebyshev frames with real entries and worst-case coherence analysis, submitted.
  • S. Li, C. Zheng, A fast and super resolution method in DOA estimation under severe noise, submitted.
  • T. Bemrose, P.G. Casazza, R. G. Lynch, The unconditional constant for Hilbert space frame expansions , submitted. pdf
  • P.G. Casazza and L.M. Woodland, The fundamentals of Spectral Tetris frame constructions , submitted. pdf
  • M. Fickus, D.G. Mixon, A.A. Nelson, Y. Wang, Phase retrieval from very few measurements , to appear in: Linear Algebra Appl. pdf
  • J. Jasper, D.G. Mixon, M. Fickus, Kirkman equiangular tight frames and codes, IEEE Trans. Inform. Theory. 60 (2014) 170-181. pdf
  • B. Alexeev, A.S. Bandeira, M. Fickus, D.G. Mixon, Phase retrieval with polarization , SIAM J. Imaging Sci. 7 (2014) 35-66. pdf

2013

  • S. Montgomery-Smith, W. Huang, A numerical method to model dynamic behavior of thin inextensible elastic rods in three dimensions, J. Comput. Nonlinear Dynam. 9 No. 1 (2013). pdf
  • S. Montgomery-Smith, H. Morgan, Obtaining laws of thermodynamics for ideal gases using elastic collisions, submitted. pdf
  • D. Edidin, A. Geraschenko, M. Satriano, There is no degree map for 0-cycles on Artin stacks, Trans. Groups, 18 No. 2 (2013) 385-389. pdf
  • B. Bodmann, Random fusion frames are nearly equiangular and tight, Lin. Alg. Appls. 439 No. 5 (2013) 1401-1414. pdf
  • B. Bodmann, P. Singh Random fusion frames for loss-insensitive packet encoding, Proc. SPIE 8858, Wavelets and Sparsity XV, 88580F/1-12, 2013.
  • S. Li, Y. Liu, T. Mi, Sparse dual frames and dual Gabor functions of minimal time and frequency supports, J. Four. Anals. Appls. 19 No. 1 (2013) 48-76. pdf
  • A.S. Bandeira, M. Fickus, D.G. Mixon, P. Wong, The road to deterministic matrices with the Restricted Isometry Property , J. Fourier Anal. Appl. 19 (2013) 1123-1149. pdf
  • M. Fickus, D.G. Mixon, M.J. Poteet, N. Strawn, Constructing all self-adjoint matrices with prescribed spectrum and diagonal , Adv. Comput. Math. 39 (2013) 585-609. pdf
  • J. Cahill, M. Fickus, D.G. Mixon, M.J. Poteet, N. Strawn, Constructing finite frames of a given spectrum and set of lengths , Appl. Comput. Harmon. Anal. 35 (2013) 52-73. pdf
  • J. Cahill, D.G. Mixon and N. Strawn, Connectivity and irreducibility of algebraic varieties of finite unit norm tight frames, submitted. pdf
  • P.G. Casazza and L.M. Woodland, Phase retrieval by vectors and projections, Contemporary Math. (to appear). pdf
  • J. Cahill, P.G. Casazza, M. Ehler, S. Li, Tight and random nonorthogonal fusion frames, submitted. pdf
  • J. Cahill, P.G. Casazza, J. Peterson, L.M. Woodland, Using projections for phase retrieval, in Wavelets and Sparsity XV, Dimitri Van De Ville; Vivek K. Goyal; Manos Papadakis, Editors, Proceedings of SPIE Vol. 8858 (SPIE, Bellingham, WA 2013), 88581W. pdf
  • P.G. Casazza, R.G. Lynch, J. Tremain, L.M. Woodland, Integer frames, Houston Journal of Math. (to appear). pdf
  • J. Cahill, P.G. Casazza, J. Peterson, L.M. Woodland, Phase retrieval by projections, Houston Journal of Math. (to appear). pdf
  • A. Bandeira, J. Cahill, D. Mixon, A. Nelson, Saving phase: Injectivity and stability for phase retrieval, submitted. pdf
  • J. Cahill, X. Chen, A note on scalable frames, submitted. pdf
  • P. G. Casazza, M. Fickus, D. Mixon, J. Peterson and I. Smalyanau, Every Hilbert space frame has a Naimark complement, J. Math. Anal. Appl. 406 (2013) 111-119. pdf

2012

  • P. Casazza, G. Pfander, Analyzing the algorithm for proving the restricted invertibility theorem, submitted. pdf
  • M. Fickus, J. Jasper, D. Mixon, J. Peterson, Group-theoretic constructions of erasure-robust frames, submitted. pdf
  • P. G. Casazza, The simplified version of the Spielman-Srivastava algorithm for proving the Bourgain-Tzafriri restricted invertibility theorem, unpublished notes. pdf
  • P. G. Casazza, G. Kutyniok, Introduction to finite frame theory, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012). pdf
  • P. G. Casazza, G. Kutyniok, Fusion frames, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012). pdf
  • P. G. Casazza, D. Speegle, Spanning and independence properties of finite frames, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012). pdf
  • P. G. Casazza, The Kadison-Singer and Paulsen problems in finite frame theory, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012). pdf
  • J. Cahill, N. Strawn, Algebraic geometry and finite frames, in Finite Frames: Theory and Applications, Eds. P. G. Casazza and G. Kutyniok, Birkhäuser, Boston (2012). pdf
  • J. C. Tremain, Intelligence, creativity and conformity, preprint (2012). pdf
  • J. C. Tremain, C. Vaidyanathan, An elementary representation of all real Hessenberg unitary matrices, preprint (2012). pdf
  • P. G. Casazza, A. Heinecke, K. Kornelson, Y. Wang, Z. Zhou, Necessary and sufficient conditions to perform spectral tetris, preprint (2012). pdf
  • P. G. Casazza, J. Peterson, Weighted fusion frame construction via spectral tetris, preprint (2012). pdf
  • P. G. Casazza, J. Peterson, An elementary, illustrative proof of the Rado-Horn theorem, Linear Algebra and its Applications 437 (2012) 2523-2537. pdf
  • J. Cahill, P. G. Casazza, G. Kutyniok, Operators and frames, preprint (2012). pdf
  • P. G. Casazza, M. Fickus and D. G. Mixon, Auto-tuning unit norm frames, Appl. Comput. Harmon. Anal. 32 (2012), p 1-15. pdf
  • P. G. Casazza, M. Fickus, A. Heinecke, Y. Wang and Z. Zhou, Spectral tetris fusion frame constructions, Jour. Fourier Anal. and Appls. 18 No. 4 (2012) 828-851. pdf

2011

  • B. Alexeev, J. Cahill, D. G. Mixon, Full spark frames, preprint (2011). pdf
  • B. G. Bodmann, J. Cahill, P. G. Casazza, Fusion frames and the restricted isometry property, preprint (2011). pdf
  • M. Fickus, D. G. Mixon, J. C. Tremain, Constructing a large family of equiangular tight frames, Proceedings of SampTA 2011, Singapore. pdf
  • B. G. Bodmann, P. G. Casazza, J. Peterson, I. Smalyanau, Fusion frames and unbiased basic sequences, preprint (2011). pdf
  • J. C. Tremain, Algorithmic constructions of unitary matrices and tight frames, preprint (2011). pdf
  • J. Cahill and P. G. Casazza, The Paulsen problem in operator theory, submitted to Operators and Matrices (2011). pdf
  • P. G. Casazza, A. Heinecke, F. Krahmer and G. Kutyniok, Optimally Sparse Frames, IEEE Trans. Inform. Theory 57 (2011), 7279-7287. pdf
  • J. Cahill, M. Fickus, D. G. Mixon, M. J. Poteet and N. K. Strawn, Constucting finite frames of a given spectrum and set of lengths, submitted (2011). pdf
  • P. G. Casazza, A. Heinecke and G. Kutyniok, Optimally sparse fusion frames: Existence and construction, Proceedings of SampTA 2011, Singapore. pdf
  • J. Cahill, P. G. Casazza and A. Heinecke, A notion of redundancy for infinite frames, Proceedings of SampTA 2011, Singapore. pdf
  • B. G. Bodmann, P. G. Casazza and G. Kutyniok, A quantitive notion of redundancy and its applications, Proceedings of SampTA 2011, Singapore. pdf
  • P. G. Casazza, M. Fickus, D. Mixon, Y. Wang and Z. Zhou, Constructing tight fusion frames, Appl. Comput. Harmon. Anal. 30 (2011) 175-187. pdf
  • B. G. Bodmann, P. G. Casazza and G. Kutyniok, A Quantitative Notion of Redundancy for Finite Frames, Appl. and Comput. Harmonic Anal. 30 (2011) 348-362. pdf
  • R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok and A. Pezeshki, Sparse Fusion Frames: Existence and Construction. Advances in Computational Mathematics, 35 No. 1 (2011) pp. 1-31. pdf

2010

  • J. Cahill, P. G. Casazza and S. Li, Non-orthogonal fusion frames and the sparsity of fusion frame operators, submitted to JFAA. pdf
  • M. Fickus, D. G. Mixon and J. C. Tremain, Steiner equiangular tight frames, preprint submitted to Linear Algebra and Applications (2010). pdf
  • B. G. Bodmann, P. G. Casazza, V. I. Paulsen and D. Speegle, Spanning and independence properties of frame partitions, Proceedings of AMS 140, No. 7 (2012), p. 2193 - 2207. pdf
  • B. G. Bodmann, P. G. Casazza and G. Kutyniok, Upper and Lower Redundancy of Finite Frames. 43nd Annual Conference on Information Sciences and Systems (CISS) (Princeton University, NJ, 2010). pdf
  • J. Cahill, P.G. Casazza and A. Heinecke, A quantitative notion of redundancy for infinite frames, preprint (2010). pdf
  • P. G. Casazza, M. Fickus, D.G. Mixon and J.C. Tremain, The Bourgain-Tzafriri conjecture and concrete constructions of non-pavable projections, submitted to: Operators and Matrices (2010). pdf
  • B. G. Bodmann and P. G. Casazza, The road to equal-norm Parseval frames. Journal of Functional Analysis, Vol. 258 (2010), p. 397-420. pdf
  • P.G. Casazza and M. Leon, Existence and Construction of Finite Frames with a Given Frame Operator, International Journal of Pure and Applied Mathematics, Vol. 63, No. 2 (2010), p. 149 - 158. pdf

2009

  • J.C. Tremain, Concrete Constructions of Real Equiangular Line Sets, preprint (2009). pdf
  • J.C. Tremain, Concrete Constructions of Equiangular Line Sets II, preprint (2009). pdf
  • J.C. Tremain, The Bourgain-Tzafriri Conjecture for Operators with Small Coefficients, preprint (2009). pdf
  • R. Calderbank, P. G. Casazza, A. Heinecke, G. Kutyniok and A. Pezeshki, Constructing Fusion Frames with Desired Parameters. Wavelets XIII (San Diego, CA, 2009), 744612-1 - 744612-10, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009. pdf
  • B. Bodmann and P.G. Casazza, When are frames close to equal-norm Parseval frames?, preprint (2009). pdf
  • P.G. Casazza, M. Fickus, D. Mixon and J.C. Tremain, Concrete Constructions of Non-Pavable Projections, preprint (2009). pdf
  • P.G. Casazza, M. Fickus, D. Mixon, Y.Wang and Z. Zhou, Constructions and existence of tight fusion frames, Proc. SPIE. 7446 (2009) 744613/1-10. pdf
  • B. Bodmann, P.G. Casazza, G. Kutyniok and S. Senger, A Low Complexity Replacement Scheme for Erased Frame Coefficients, Wavelets XIII (San Diego, CA, 2009), 74460O-1 - 74460O-10, SPIE Proc. 7446, SPIE, Bellingham, WA, 2009. pdf
  • P.G. Casazza and G.E. Pfander, Infinite Dimensional Restricted Invertibility, preprint. pdf
  • B. Bodmann, P.G. Casazza, G. Kutyniok and S. Senger, Error Correction for Erasures of Quantized Frame Coefficients, SampTA'09 (Marseille, France, 2009), Proc., 2009. pdf
  • P.G. Casazza and M. Fickus, Gradient descent of the frame potential, Proc. Sampl. Theory Appl. (2009). pdf
  • R. Balan, P. Casazza and Z. Landau, Redundancy for localized and Gabor frames, preprint. pdf
  • P.G. Casazza and M. Fickus, Minimizing Fusion Frame Potential, Acta Applicandae Mathematicae, Volume 107, Numbers 1-3 (2009), pp. 7-24. pdf
  • P.G. Casazza and J.C. Tremain, Revisiting the Bourgain-Tzafriri Restricted Invertibility Theorem, Operators and Matrices, Vol. 3, No. 1 (2009), 97-110. pdf
  • P.G. Casazza, S. Obeidat, S. Samarah and J.C. Tremain, Sums of Hilbert Space Frames, J. Math. Analysis and Appl. Vol. 351, Issue 2 (2009), 579-585. pdf
  • P.G. Casazza, A Mathematician's Survival Guide, preprint. pdf
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