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Alexander Kheifets


Alexander Kheifets
Professor Alexander KheifetsProfessor

Research Interests

Complex Analysis, Harmonic Analysis, Operator Theory, Hilbert spaces of analytic functions, Jacobi matrices, scattering

Inverse scattering for Jacobi and CMV matrices. Functional models (Nagy- Foias ,de Branges- Rovnyak, Hellinger). Interpolation in classes of analytic and harmonic functions. Problems of Complex Analysis involving geometry of operators on Hilbert space are of particular interest.

Education

  • Ph D: Mathematics, (1990), Kharkov National University - Ukraine
    Dissertation/Thesis Title: Scattering Matrices and Parseval Equality in Abstract Interpolation Problem
  • MS: Mathematics, (1978), Kharkov National University - Ukraine
    Dissertation/Thesis Title: Algorithm for Darlington Representation of Rational Matrix-functions

Selected Awards and Honors

  • Excellence in Teaching Award (2004), Teaching - UMass Lowell Department of Mathematics
  • Prize for Young Mathematicians (with Peter Yuditskii) (1987), Scholarship/Research - Kharkov Mathematical Society

Selected Publications

  • Boiko, S., Dubovoy, V., Kheifets, A. (2015). On Some Special Cases of the Radon–Nikodym Theorem for Vector-and Operator-valued Measures (244: pp. 131–147). Operator Theory: Advances and Applications
  • Boiko, S., Dubovoy, V., Kheifets, A. (2014). Defect Functions of Holomorphic Contractive Operator Functions and the Scattering Suboperator Through the Internal Channels of a System: Part II. Complex Analysis and Operator Theory, 8(5) 991–1036.
  • Ball, J.A., Kheifets, A. (2013). The inverse commutant lifting problem. II: Hellinger functional-model spaces. Complex Analysis and Operator Theory, 7(4) 873–907.
  • Jones, L.K., Zou, F., Kheifets, A., Rybnikov, K., Berry, D., Tan, A.C. (2011). Confident Predictability: Identifying reliable gene expression patterns for individualized tumor classification using a local minimax kernel algorithm. BMC medical genomics, 4(1) 10.
  • Ball, J.A., Kheifets, A. (2011). The Inverse Commutant Lifting Problem. I: Coordinate-Free Formalism. Integral Equations and Operator Theory, 70(1) 17-62.
  • Ball, J.A., Kheifets, A. (2011). The Inverse Commutant Lifting Problem. II: Hellinger Functional-Model Spaces. Complex Analysis and Operator Theory, 1-35.
  • Kheifets, A., Propp, J. (2010). A counterexample to integration by parts. Mathematics Magazine, 83(3) 222-225.
  • Bolotnikov, V., Kheifets, A. (2009). Carath odory-Julia type conditions and symmetries of boundary asymptotics for analytic functions on the unit disk. Mathematische Nachrichten, 282(11) 1513-1536.
  • Bolotnikov, V., Kheifets, A. (2008). Carath odory-Julia type theorems for operator valued Schur functions. Journal d'Analyse Mathematique, 106(1) 237-270.
  • Bolotnikov, V., Kheifets, A. (2006). A higher order analogue of the Carath odory-Julia theorem. Journal of Functional Analysis, 237(1) 350-371.
  • Bolotnikov, V., Kheifets, A. (2006). On negative inertia of pick matrices associated with generalized schur functions. Integral Equations and Operator Theory, 56(3) 323-355.
  • Bolotnikov, V., Kheifets, A., Rodman, L. (2004). Jet functions having indefinite Carath odory-Pick matrices. Linear Algebra and Its Applications, 385(1-3) 215-286.
  • Bolotnikov, V., Kheifets, A., Rodman, L. (2004). Nevanlinna-Pick interpolation: Pick matrices have bounded number of negative eigenvalues. Proceedings of the American Mathematical Society, 132(3) 769-780.
  • Bolotnikov, V., Kheifets, A., Rodman, L. (2004). Operator-valued jet functions with positive carath odory-pick operators. Integral Equations and Operator Theory, 50(3) 291-304.
  • Bolotnikov, V., Kheifets, A., Rodman, L. (2003). Pairs of functions with indefinite Pick matrices. Linear Algebra and Its Applications, 367 271-290.
  • Kheifets, A. (1996). Hamburger moment problem: Parseval equality and A-singularity. Journal of Functional Analysis, 141(2) 374-420.
  • Kheifets, A. (1995). On a necessary but not sufficient condition for a -generating pair to be a nehari pair. Integral Equations and Operator Theory, 21(3) 334-341.
  • Kheifets, A. (1995). On Regularization of -Generating Pairs. Journal of Functional Analysis, 130(2) 310-333.
  • Kheifets, A. (1992). The generalized bitangential Schur-Nevanlinna-Pick problem and the related parseval equality. Journal of Soviet Mathematics, 58(4) 358-364.
  • Kheifets, A. (1990). Parseval's equality in the abstract interpolation problem and the coupling of open systems. I. Journal of Soviet Mathematics, 49(4) 1114-1120.
  • Kheifets, A. (1990). Parseval's equality in the abstract interpolation problem and the coupling of open systems. II. Journal of Soviet Mathematics, 49(6) 1307-1310.

Selected Presentations

  • - Complex Analysis, Operator Theory and Approximation, 2011 - Linz, Austria
  • - International Conference on Modern Analysis, 2011
  • - Complex Analysis, 2010 - Lviv, Ukraine
  • - 25 Years of Schur Analysis in Leipzig, 2009 - Leipzig, Germany
  • - B. Simon Seminar on Mathematical Physics, 2009 - Pasadena, CA
  • - Ukrainian Mathematical Congress, 2009 - Kiev, Ukraine
  • - 19-th International Workshop on Operator Theory And Applications (IWOTA), 2008 - Williamsburg, VA
  • - Operator Theory Analysis and Mathematical Physics (OTAMP), 2008 - Bedlewo, Poland
  • - 16-th Summer St.-Petersburg Meeting in Mathematical Analysis (Satellite of the Euler Congress), 2007 - St. Petersburg, Russia
  • - Characteristic Functions and Transfer Functions in Operator Theory and System Theory, 2007 - Beer-Sheva, Israel
  • - Entire and Subharmonic Functions and Related Topics (B.Levin Centennial Conference), 2006 - Kharkov, Ukraine
  • - 16-th International Workshop on Operator Theory And Applications (IWOTA), 2005 - Storrs, CT
  • - 15-th International Workshop on Operator Theory And Applications (IWOTA), 2004 - Newcastle, UK
  • - 13-th International Workshop on Operator Theory And Applications (IWOTA), 2002 - Blacksburg, VA
  • - Mathematical Theory of Networks and Systems (MTNS), 2002 - South Bend, IN
  • - Multivariable System and Operator Theory, 2001 - Beer-Sheva, Israel
  • - 11-th International Workshop on Operator Theory And Applications (IWOTA), 2000 - Bordeaux, France
  • - Conference in Honor of H. DymÕs 60Õs Anniversry, 1999 - Rehovot, Israel
  • - 10-th International Workshop on Operator Theory And Applications (IWOTA), 1998 - Groningen, Netherlands
  • - Mathematical Theory of Networks and Systems (MTNS), 1998 - Padova, Italy
  • - Entire and Subharmonc Functions (In memory of B. Levin), 1997 - Kharkov, Ukraine
  • - International Conference in Honor of M. Livsits 80s Anniversary, 1997 - Beer-Sheva, Israel
  • - International Conference in Memory of M. Krein, 1997 - Odessa, Ukraine
  • - 9-th International Workshop on Operator Theory, 1996 - Bloomington, IN
  • - International Seminar on Complex Analysis, 1996 - Ashqelon, Israel
  • - Mathematical Theory of Networks and Systems (MTNS), 1996 - Saint Louis, MO
  • - Holomorphic Spaces Program, 1995 - Berkeley, CA
  • - International Conference in Memory of V. Potapov, 1994 - Leipzig, Germany