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Alexander Kheifets

Alexander Kheifets is a Professor in the Mathematical Sciences Department at UMass Lowell.
Alexander Kheifets Professor

Expertise

Harmonic & complex analysis, operator theory

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