Home Page of Maxim Zinchenko

Contact Info:

Address:   University of Central Florida
  Department of Mathematics
  4000 Central Florida Blvd.
  P.O. Box 161364
  Orlando, FL 32816-1364
  Office:  MAP 321
  Phone:  (407) 823-5251
  Email:  maxim (at) math.ucf.edu

Research Interests:

  • Mathematical Physics
  • Differential and Difference Equations
  • Spectral and Inverse Spectral Theory
  • Operator Theory
  • Nontrigonometric harmonic analysis
  • Orthogonal Polynomials
  • Approximation Theory

NSF Grant:

Publications and Preprints: [ArXiv] [UCD Archiv] [MP Archiv] [MathSciNet]

  • Boundary data maps and Krein's resolvent formula for Schrödinger operators on a compact interval; with Stephen Clark, Fritz Gesztesy, and Roger Nichols. [PDF]
  • On a class of model Hilbert spaces; with Fritz Gesztesy and Rudi Weikard. To appear in Discrete Contin. Dyn. Syst. [PDF]
  • Initial value problems and Weyl-Titchmarsh theory for Schrödinger operators with operator-valued potentials; with Fritz Gesztesy and Rudi Weikard. To appear in Oper. Matrices. [PDF]
  • Finite gap Jacobi matrices, III. Beyond the Szegö Class; with Jacob Christiansen and Barry Simon. Constr. Approx. 35 (2012), 259-272. [PDF]
  • Symmetrized perturbation determinants and applications to boundary data maps and Krein-type resolvent formulas; with Fritz Gesztesy. Proc. London Math. Soc. 104 (2012), 577 – 612. [PDF]
  • Finite gap Jacobi matrices, II. The Szegö Class; with Jacob Christiansen and Barry Simon. Constr. Approx. 33 (2011), 365 - 403. [PDF]
  • The Hilbert transform of a measure; with Alexei Poltoratski and Barry Simon. J. d'Analyse Math. 111 (2010), 247-265. [PDF]
  • Finite gap Jacobi matrices, I. The isospectral torus; with Jacob Christiansen and Barry Simon. Constr. Approx. 32 (2010), 1-65. [PDF]
  • The inverse resonance problem for CMV operators; with Rudi Weikard. Inverse Problems. 26 055012 (2010). [PDF]
  • Trace formulas and a Borg-type theorem for CMV operators with matrix-valued coefficients. Math. Nachr. 283 (2010), 312-329. [PDF]
  • On Dirichlet-to-Neumann maps, nonlocal interactions, and some applications to Fredholm determinants; with Fritz Gesztesy and Marius Mitrea. Few-Body Syst. 47 (2010), 49-64. [PDF]
  • Right limits and reflectionless measures for CMV matrices; with Jonathan Breuer and Eric Ryckman. Commun. Math. Phys. 292 (2009), 1-28. [PDF]
  • Finite gap Jacobi matrices: An announcement; with Jacob Christiansen and Barry Simon. J. Comput. Appl. Math. 233 (2009), 652-662. [PDF]
  • Minimal rank decoupling of full-lattice CMV operators with scalar- and matrix-valued Verblunsky coefficients; with Stephen Clark and Fritz Gesztesy. In Proceeding of the 14th International Conference on Difference Equations and Applications, Istanbul, 2008, M. Bohner, Z. Dosla, G. Ladas, M. Unal, and A. Zafer (eds.), Difference Equations and Applications, Ugur-Bahcesehir University Publishing Company, Istanbul, Turkey, 2009, pp. 19-59. [PDF]
  • Local spectral properties of reflectionless Jacobi, CMV, and Schrödinger operators; with Fritz Gesztesy. J. Diff. Eqs. 246 (2009), 78-107. [PDF]
  • Borg-Marchenko-type uniqueness results for CMV operators; with Stephen Clark and Fritz Gesztesy. Trans. R. Norw. Soc. Sci. Lett. 1 (2008), 1-18. [PDF]
  • Essential closures and AC spectrum for reflectionless Jacobi, CMV, and Schrödinger operators; with Fritz Gesztesy and Konstantin Makarov. Acta Appl. Math. 103 (2008), 315-339. [PDF]
  • On Dirichlet-to-Neumann maps and some applications to modified Fredholm determinants; with Fritz Gesztesy and Marius Mitrea. In Proceedings of the conference on Operator Theory, Analysis in Mathematical Physics - OTAMP 2006, J. Janas, P. Kurasov, A. Laptev, S. Naboko, and G. Stolz (eds.), Operator Theory: Advances and Applications, Vol. 78, Birkhäuser, Basel, 2008, pp. 191-215. [PDF]
  • Variations on a theme of Jost and Pais; with Fritz Gesztesy and Marius Mitrea. J. Funct. Anal. 253 (2007), 399-448. [PDF]
  • A multi-dimensional variant of the Jost and Pais formula; with Fritz Gesztesy and Marius Mitrea. Rep. Math. Phys. 59 (2007), 365-377. [PDF]
  • Weyl-Titchmarsh theory and Borg-Marchenko-type uniqueness results for CMV operators with matrix-valued Verblunsky coefficients; with Stephen Clark and Fritz Gesztesy. Oper. Matrices 1 (2007), 535-592. [PDF]
  • A Borg-type theorem associated with orthogonal polynomials on the unit circle; with Fritz Gesztesy. J. Lond. Math. Soc. (2) 74 (2006), 757-777. [PDF]
  • Weyl-Titchmarsh theory for CMV operators associated with orthogonal polynomials on the unit circle; with Fritz Gesztesy. J. Approx. Th. 139 (2006), 172-213. [PDF]
  • On spectral theory for Schrödinger operators with bly singular potentials; with Fritz Gesztesy. Math. Nachr. 279 (2006), 1041-1082. [PDF]
  • Non-self-adjoint operators, infinite determinants, and some applications; with Fritz Gesztesy, Yuri Latushkin, and Marius Mitrea. Russ. J. Math. Phys. 12 (2005), 443-471. [PDF]

Teaching:

  • SP 2011-12, MAA 6405, Complex Variables
  • FA 2011-12, MAA 6306, Real Analysis
  • FA 2011-12, MAP 2302, Differential Equations
  • SP 2010-11, MAP 4307, Applied Complex Variables
  • FA 2010-11, MAC 2312, Calculus II
  • FA 2010-11, MAC 2313, Calculus III
  • SP 2009-10, Math 1700, Calculus I for science and engineering
  • FA 2009-10, Math 1220, Honors Calculus I for social sciences
  • FA 2009-10, Math 5070, Numerical Analysis I
  • SP 2008-09, Math 111c, Advanced Topics in Analysis
  • FA 2008-09, Math 108a, Classical Analysis I
  • FA 2008-09, Math 142a, Partial Differential Equations
  • SP 2007-08, Math 140c, Functional Analysis
  • WI 2007-08, Math 108b, Classical Analysis II
  • FA 2007-08, Math 145a, Introduction to Unitary Group Representations
  • SP 2006-07, Math 191c, Topics in Spectral and Inverse Spectral Theory
  • WI 2006-07, Math 108b, Classical Analysis II
  • FA 2006-07, Math 108a, Classical Analysis I
  • SU 2005-06, Math 4100, Differential Equations