John Shijun Zheng

Department of Mathematical Sciences

Georgia Southern University
     Phone: (912) 478-1338
Statesboro, GA 30460
     szheng at GeorgiaSouthern dot edu

Professional Experience
Research Interests
Lecture Notes
Selected Publications
Preprints
Technical Reports
Education
Invited Talks
Professional Activities

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Professional Experience


      

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Research Interests

Harmonic analysis and PDE, Schrödinger operators, Wavelet method in numerical PDEs, Mathematical modeling
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Lecture Notes


          Lecture on Schrödinger operators:  Harmonic analysis and PDE    (in preparation).

         Topics in Geometric analysis and Mathematical Physics

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    Selected Publications

    1. Spectral multipliers for Schrödinger operators. Illinois Journal of Mathematics 54, No.2. 
    2. Littlewood-Paley theorem for Schrödinger operators. Anal. Theo. Appl. 22(4), 2006. Archiv
    3. (with J.J. Benedetto) Besov spaces for the Schrödinger operator with barrier potential. Complex Analysis and Operator Theory (2010). Archiv
    4. (with G.Olafsson) Function spaces associated with Schrödinger operators: the Pöschl-Teller potential.
      Journal of Fourier Analysis and Applicaitons 12 (6), 2006. Archiv
    5. A representation formula related to Schroedinger operators.  Anal. Theo. Appl., 20(3), (2004) also in Archiv
    6. Perturbed Fourier transform associated to Schrodinger operators. (to be submitted).
    7. Dissertation, Besov spaces for Schrödinger operators. University of Maryland, College Park, (2003).
    8. Cesaro summability of Hardy space on the ring of integers in a local field. J. Math. Anal. Appl., 249, (2000).
    9. Riesz type kernels over the ring of integers of a local field. J. Math. Anal. Appl., 208, (1997).
    10. (with Weiyi Su), L^p estimates for the iterated Hardy-Littlewood maximal operator. Approx. Theory Appl., 14 (3), (1998).
    11. L^p estimates for the iterated Hardy-Littlewood maximal operator, II
    12. (with Weixing Zheng), Almost everywhere convergence of sequences of multiplier operators on local fields. Science in China, 40 (1), (1997). Springer-Verlag.
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      Preprints

      1. Dispersive estimates for Schrödinger and wave equations with potentials near Ln/2(Rn) (In preparation) 2006.
      2. (with G. Olafsson and K. Oskolkov) Spectral multipliers for Schrödinger operators, II (In preparation).
      3. (with G. Olafsson) Wavelets, Besov spaces and integral representations
      4. (with Z. Zhang) Strichartz estimates for Schrodinger equation with magnetic potential of polynomial growth, (in preparation)
      5. (with D.M. Healy and I. Konstantinidis) Wavelet transform for anisotropic diffusion modeling in image processing, I
      6. Facet Modeling of 2D Equilibrium Crystals
      7. Multipliers of Hardy spaces on local fields
      8. Weak type estimates of Bochner-Riesz means on Riemannian symmetric spaces
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      Technical Reports

      1. (with J.J. Benedetto, D.M. Healy and I. Konstantinidis) Report on recent progress on the TAIP project (Thin Film Analog Image Processing), 2003 (DARPA (Defense Advanced Research Projects Agency) funded project)
      2. (with Harris Wong) Facet modeling for 2D equilibrium crystal solid film, 2004 (CCT (Center for Computaton and Technology) funded project)
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      Education

      Ph.D., University of Maryland, 2003
                M.A., University of New Mexico, 1997

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      Invited Talks

      1. Besov spaces associated with Schroedinger operators, University of California at Los Angeles, Los Angeles, March, 2002.
      2. Schroedinger operators, Besov spaces and Wavelet computations for thin film image processing, Colloquium talk, University of Houston, Houston, November, 2002.
      3. Wavelet computing for semigroup operators, NSF FRG workshop on Wavelets, Frames, and Operator Theory, University of Maryland, College Park, January, 2003.
      4. Operator reconstruction in wavelet basis and its applications in PDEs, The Sixth International Joint Meeting of the AMS and the SMM, Houston, May, 2004.
      5. Operator representations in wavelet basis and applications in PDEs, The Second International Conference on Computational Harmonic Analysis, Nashville, May 24-30, 2004.
      6. Multiscale operator reconstructions and time-dependent PDEs, Princeton University, April, 2005.
      7. Spectral multipliers for Schrödinger operators. AMS Special Session on Harmonic Analysis: Trends and Perspectives, Salt Lake City, Utah, October 7-8, 2006
      8. Spectral calculus for Schrödinger operators in one and three dimensions. Johns Hopkins University, Baltimore, November 5-7, 2006
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      Professional Activities

      Membership: AMS and SIAM
        Editorial Boards: Advances in Pure Mathematics,
                                      Applied Mathematics
                                                Current Advances in Mathematics
                                      Pioneer Journal of Mathematics and Mathematical Sciences
                                      Pioneer Journal of Algebra, Number Theory and its Applications
                                                International Journal of Advanced Mathematical Sciences
                                                International Journal of Advanced Mathematics and Physics                              

                     Referee for: Jour. Functional Analysis, Jour. Math. Anal. Appl., Jour. Differential Equations, Jour. Geometric Analysis, Communications on Pure Applied Analysis, Jour. Approx. Theory, Current Advances in Mathematics, Advances in Pure Mathematics, Anal. Theory Appl., Approx. Theory Appl., Acta Mathematica Scientia, Contemporary Mathematics, Publicationes Mathematicae, Jour. Math. Soc. Japan, Intern.Jour.Math. Math Sci., American Journal of Applied Mathematics, Applied Mathematical Modelling

                 Reviewer for:
         Mathematical Reviews
        Conferences:
      TBA
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      August, 2007