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Flavia Colonna

Professor

Office: Exploratory Hall, room 4215

Phone: (703) 993-1465

Fax: (703) 993-1491

E-mail: fcolonna@gmu.edu

Personal Homepage:
http://mason.gmu.edu/~fcolonna

Education

  • Ph. D.,1985, University of Maryland, College Park, Complex Analysis

Research

  • Complex Analysis
  • Discrete Harmonic Analysis

  • Potential Theory and Integral Geometry

  • Operator Theory

Selected Publications

  • Multiplication Operators between the Lipschitz Space and the Space of Bounded Functions on a Tree, with G.R. Easley, Mediterr. Journal Math., to appear
  • Hints on How to Improve Mathematics Instruction, with G.R. Easley, Journal of e-Learning and Knowledge Society, to appear
  • Biharmonic Extensions on Tress withour Positive Potentials, with I. Bajunaid, J.M. Cohen and D. Singman, Journal Math Anal. Appl., to appear
  • Multiplication Operators on the Weighted Lipschitz Space of a Tree, with R.F. Allen and G.R. Easley, Journal Operator Theory, to appear
  • Multiplication Operators on the Weighted Lipschitz Space of a Tree, with G.R. Easley, Integral Equations and Operator Theory, 68 (3) (2010), pp. 391-411
  • Radon Transform Inversion via the Shearlet Representation, with G.R. Easley, K. Guo and D. Labate, Appl. Comput. Harmon. Anal., 29 (2010), pp. 232-250
  • Weighted Composition Operators from H to the Bloch Space of a Bounded Homogeneous Domain, with R.F. Allen, Integral Equations and Operator Theory, 66 (1) (2010), pp. 21-40
  • Weighted Composition Operators on the Bloch Space of a Bounded Homogeneous Domain, with R.F. Allen, Operator Theory: Advances and Applications 202 (2009), pp. 11-37, Birkhauser Verlag, Basel, Switzerland
  • Classification of Brelot Structures on Graphs, with I. Bajunaid, J.M. Cohen and D. Singman, Adv. Appl. Math., 43 (2009), pp.113-136
  • Multiplication Operators on the Bloch Space of Bounded Homogeneous Domains, with R.F. Allen, Comput. Methods Funct. Theory, 9 (2) (2009), pp. 679-693
  • Biharmonic Green Function on Homogeneous Trees, with J.M. Cohen and D. Singman, Mediterr. J. Math, 6 (3) (2009), pp. 249-272
  • On the Isometric Composition Operators in the Bloch Space in C^n, with R.F. Allen, J. Math. Anal. Appl., 355 (2009), pp. 675-688
  • Improved Radon Based Imaging Using the Shearlet Transform, with G.R. Easley and D. Labate.  Proc. SPIE 2009, Independent Component Analysis, Wavelets, Neural Networks, Biosystems, and Nanoengineering VII, 7343 (2009), Orlando
  • Characterization of Isometries and Spectra of Multiplication Operators on the Bloch Space, with R.F. Allen.  Bull Austral. Math. Soc., 79 (2009), pp. 147-160
  • Shearlet Based Total Variation for Denoising, with G.R. Easley and D. Labate.  IEEE Trans. Image Processing, 18 (2) (2009), pp. 260-268
  • Characterization of Harmonic Structures on Graphs, with I. Bajunaid, J.M. Cohen and D. Singman.  Adv. Appl. Math., 43 (2009), pp. 113-136

  • A Riesz Decomposition Theorem on Harmonic Spaces without Positive Potentials, with I. Bajunaid, J.M. Cohen, and D. Singman.  Hiroshima Math J., 38 (2008), pp. 37-50

  • Generalized Discrete Radom Transforms and Applications to Image Processing, with G.R. Easley.  Advances in Image Processing and Electron Physics, 151 (2008), pp. 169-239

  • Isometric Composition Operators on the Bloch Space in the Polydisk, with J.M. Cohen.  Contemporary Mathematics, Banach Spaces of Analytic Functions, 454 (2008), pp. 9-21

  • Improved Total Variation Algorithms for Wavelet-Based Denoising, with G.R. Easley.  Proc. SPIE 2007, Independent Component Analyses, Wavelets, Unsupervised Smart Sensors, and Neural Networks V (2007), Orlando

  • A Global Riesz Decomposition Theorem on Trees without Positive Potentials, with J.M. Cohen and D. Singman.  J. London Math. Soc. (2) 75 (2007), pp. 1-17

  • Preimages of One-Point Sets of Bloch and Normal Functions, with J.M. Cohen.   Mediterranean J. Math.  (3) (2006), pp. 513-532

  • Characterisation of the Isometric Composition Operators on the Bloch Space, Bull. Austral. Math. Soc. 72 (2005) pp. 283-290

  • Function Series, Catalan Numbers, and Random Walks on Trees, with I. Bajunaid, J.M. Cohen, and D. Singman.  American Mathematical Monthly, 112 (2005), pp. 765-785

  • Generalized Discrete Radon Transforms and their use in the Ridgelet Transform, with G.R. Easley.  Journal of Mathematical Imaging and Vision, 23 (2005), pp. 145-165

  • Multichannel Deconvolution Problem: A Discrete Analysis, with G.R. Easley. Journal of Fourier Analysis and Applications, 10 (2004), pp. 351-376

  • Invariant Object Recognition Base on the Generalized Discrete Radon Transforms, with G.R. Easley. Proc. SPIE 2004, Independent Component Analyses, Wavelets, Unsupervised Smart Sensors, and Neural Networks II, 5439 (2004), Orlando, pp. 164-174

  • Distributions and Measures on the Boundary of a Tree, with J.M. Cohen and D. Singman. Journal Math. Anal. and Appl., 293 (2004), pp. 89-107

  • Geometric Transforms and their Applications to SAR Speckle Reduction, with G.R. Easley. Proc. SPIE 2003, Algorithms for Synthetic Aperture Radar Imagery X, 5095 (2003)

  • Trees as Brelot Spaces, with I. Bajunaid, J.M. Cohen, and D. Singman. Advances in Appl. Math., 30 (2003), 706-745

  • Analytic Eigendistributions and Applications to Homogeneous Trees, with J.M. Cohen. Advances in Appl. Math., 29 (2002), 999-1043

Professional Awards and Invitations

  • Lester R. Ford Award, Mathematical Association of America, 2006 for the article Function series, Catalan numbers, and random walks on trees

  • First Annual GMU Mosaic Outstanding Faculty Award, 2003

  • Summer Research Grant, GMU, 1993

  • NSF Funding for CBMS Conference, Spring 1992

Recent Master's and Ph.D. Committees

  • Toan Khuu, MS student in Mathematics, thesis advisor

  • Jeremy Heil, Ph.D. student in Mathematics
  • Robert Allen, Ph.D., thesis advisor (May 2009)
  • Catherine Sausville, MS (May 2008)

  • Mohammed Buhimi, MS (May 2006)

  • Julie Hiles, M.S. thesis advisor (May 2006)

  • Mao-Tsuen Jeng, Ph.D. student in Mathematical Sciences from Fall of 2005

  • Swaponil Banerjee, Ph.D. student in Physical Sciences

  • James Kelliher, M.S. thesis advisor (May 2000)

  • James Lyons, M.A. (Dec. 1999)

  • Rolando Castro, Ph.D. in CSI (May 1999)

Invited Talks and Colloquium Lectures

  • SEAM XXVII, Florida State University, Gainesville, FL, March 2011

  • George Mason University, Colloquium, March 2011
  • George Mason University, Math Club, December 2010
  • Special Session on Operator Theory, AMS Sectional Meeting, Richmond, VA, November 2010
  • University of Bari, Colloquium, July 2010
  • George Mason University, Colloquium, April 2010
  • Multiplication Operators on the Bloch Space, University of Bari, July 2009

  • Weighted Composition Operators on the Bloch Space in C^n.  AMS Special Session on Function Theoretic Operator Theory, Joint Mathematics Meeting, Washington, DC,  January 2009

  • Characterization of Harmonic Structures on Intervals, Analysis Seminar, George Washington University, December 2008

  • An Itenary through Pure and Applied Mathematics, SIAM Fall Research Symposium, George Mason University, November 2008

  • Operator Theory on the Bloch Space, Colloquium, George Mason University, October 2008

  • A Trek in Mathematics, WISDOM (Women in Scientific Domains), sponsored by NSF, George Mason University, April 2008

  • Classification of Harmonic Structures on Intervals, Colloquium, George Mason University, November 2007
  • Isometric Composition Operators on the Bloch Space in Higher Dimensions, Complex Analysis and Potential Theory Seminar, George Mason University, November 2007
  • The Spectrum of an Isometric Composition Operator on the Bloch Space, University of Bari, July 2007.

  • Isometric Composition Operators on the Bloch Space in C^n, AMS Special Session on Complex Dynamics and Function Theory, Oxford, OH, March 16, 2007

  • Isometric Composition Operators on the Bloch Space on a Bounded Symmetric Domain, SEAM XXIII, Univ. of Richmond, March 9, 2007
  • The Best of Both Worlds:  Complex Analysis and Discrete Potential Theory, Math Club, George Mason University, December 7, 2006
  • The Bloch Space on Bounded Symmetric Domains in C^n and a Problem in Operator Theory, Graduate Student Seminar, George Mason University, September 26, 2006.
  • Isometric Composition Operators on the Bloch Space in the Polidisk, University of Bari, July 2006

  • Characterization of the Isometric Composition Operators on the Bloch Space, AMS Special Session on Banach Spaces of Analytic Functions, Durham, NH, April 2006

  • Canonical Factorization of Analytic Functions in the Complex Plane, George Mason University, February 2006

  • Function Series, Catalan Numbers, and Random Walks on Trees, George Mason University, October 2005

  • Isometric Composition Operators on the Bloch Space, University of Bari, July 2005

  • A Non-Analytic Power Series and Applications to Random Walks on Trees, University of Bari, July 2004
  • Trees as Brelot Spaces, George Mason University, November 2003

  • Trees as Brelot Spaces, University of Bari (Italy), July 2002

  • Polyharmonic Functions on Trees, Special Session on Potential Theory, AMS Sectional Meeting, Montreal, Quebec (Canada), May 2002

  • Polyharmonic Functions and Polymartingales on Trees, Annual Harmonic Analysis Conference, Sorrento, (Italy), May 2001

 

 

   
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