John Shijun Zheng's Credential's

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

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

Return to my homepage

Professional Experience

Assistant Professor, Department of Mathematical Sciences, Georgia Southern University, 2007-present.
Visiting Scholar, Brown University, Fall 2025.
IAS Visiting Member (short term) at Princeton, May 2017
Visiting Associate Professor, Brown University, Fall 2015.
Visiting Scholar, Institute of Mathematical Science, Nanjing University, May-June, 2014 and 2018.
Professeur Invitè, Université de Nantes, Laboratoire de mathématiques Jean Leray, France, July 2009.
MSI Visiting Fellow, Australian National University, Canberra, March 2009.
Postdoctoral Fellow, Department of Mathematics, University of South Carolina, 2005-2007.
Postdoctoral Associate, Department of Mathematics, Louisiana State University, 2003-2005.
Visited Princeton University, April, 2005.
Visited University of California, Los Angeles, March 2002.

Return to top of page

Research Interests

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

Return to top of page

Lecture Notes

Topics in Geometric analysis and Mathematical Physics

Return to top of page

Selected Publications

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

Preprints
1. Dispersive estimates for Schrödinger and wave equations with potentials near L^n/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
Return to top of page

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)
Return to top of page

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

Return to top of page

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
Return to top of page

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 Zb MATH (Zentralblatt MATH)

Conferences:

TBA

Return to top of page

August, 2007