Vladimir Bolotnikov, Department of Mathematics

Jones Hall Room 129, College of William and Mary,
P.O.Box 8795, Williamsburg, Virginia 23187-8795, USA
Tel: (757) 221-2009, Fax: (757) 221-2988, E-mail: vladi@math.wm.edu

Education and Current Position:

• Ph.D. (1996). Ben-Gurion University of the Negev.
• Professor of Mathematics, Department of Mathematics .

Teaching:

• Course information:
• Math 316 Geometry and Arts
Math 311 Elementary Analysis

---

Research:

• General areas: Operator Theory, Complex Analysis, Matrix Analysis.
• Publications:
• Refereed Research Papers
• Other Publications

---

Recent papers (since 2006):

• A constrained Nevanlinna-Pick interpolation problem for matrix-valued functions, to appear in Indiana Math. J. (with J.A. Ball and S. ter Horst). pdf file
• Caratheodory-Julia type conditions and symmetries of boundary asymptotics for analytic functions on the unit disk, to appear in Math. Nachr. (with A. Kheifets). pdf file
• An algorithm for finding low degree rational solutions of the Schur coefficient problem, to appear in Fuctiones et Approximatio. pdf file
• On boundary angular derivatives of an analytic self-map of the unit disk, C. R. Acad. Sci. Paris, Ser. I, 347 (2009), 227--230. pdf file
• Boundary rigidity for a class of meromorphic functions on the unit disk, Operators and Matrices 3 (2009), no. 2, 283--301. pdf file
• Nevanlinna-Pick meromorphic interpolation: the degenerate case and minimal norm solutions, J. Math. Anal. Appl. 353 (2009), 642-651. pdf file
• Interpolation problems for Schur multipliers on the Drury-Arveson space: from Nevanlinna-Pick to Abstract Interpolation Problem}, Integral Equations Operator Theory 62 (2008), no. 3, 301-349 (with J. A. Ball). pdf file
• Caratheodory-Julia type theorems for operator valued Schur functions, J. d'Analyse Mathematique 106 (2008), 237--270 (with A. Kheifets). pdf file
• A boundary analogue of the Caratheodory-Schur interpolation problem, Proc. Amer. Math. Soc. 136 (2008), no. 9, 3121-3131. pdf file
• A uniqueness result on boundary interpolation, Proc. Amer. Math. Soc. 136 (2008), no. 5, 1705-1715. pdf file
• The higher order Caratheodory--Julia theorem and related boundary interpolation problems, Operator Theory: Advances and Applications, 179 (2008), 63--102 (with A. Kheifets). pdf file
• Schur-class multipliers on the Arveson space: de Branges-Rovnyak reproducing kernel spaces and commutative transfer-function realizations, J. Math. Anal. Appl. 341 (2008), 519--539 (with J. A. Ball and Q. Fang). pdf file
• Multivariable backward-shift-invariant subspaces and observability operators, Multidimens. Syst. Signal Process. 18 (2007), no. 4, 191--248 (with J. A. Ball and Q. Fang). pdf file
• Schur-class multipliers on the Fock space: de Branges-Rovnyak reproducing kernel spaces and transfer-function realizations, in: {\em Operator Theory, structured matrices and dilations, pp. 85--114, Theta, Bucharest, 2007 (with J. A. Ball and Q. Fang). pdf file
• Transfer-function realization for multipliers of the Arveson space, J. Math. Anal. Appl. 333 (2007), no. 1, 68--92 (with J. A. Ball and Q. Fang). pdf file
• Interpolation in the noncommutative Schur-Agler class, J. of Operator Theory 58 (2007), no. 1, 83--126 (with J. A. Ball) pdf file
• Boundary Nevanlinna--Pick interpolation problems for generalized Schur functions, Operator Theory: Advances and Applications 165 (2006), 67--119 (with A. Kheifets). pdf file
• On boundary interpolation for matrix Schur functions, Mem. Amer. Math. Soc. 181 (2006), no. 856 (with H. Dym). pdf file
• A higher order analogue of the Caratheodory-Julia theorem, J. Funct. Anal. 237 (2006), no. 1, 350--371 (wth A. Kheifets). pdf file
• On negative inertia of Pick matrices associated with generalized Schur functions}, Integral Equations Operator Theory 56 (2006), no. 3, 323--355 (with A. Kheifets). pdf

---

Some older papers:

• On degenerate Hamburger moment problem and extensions of nonnegative Hankel matrices. Integral Equations Operator Theory, 25 (1996), No. 3, 253--276 (revised version). pdf file
• On degenerate interpolation, maximum entropy and extremal problems for matrix Schur functions. Integral Equations Operator Theory, 32(1998), No. 4, 367--435 (with H. Dym) pdf file
• On an operator approach to interpolation problems for Stieltjes functions. Integral Equations Operator Theory, 35(1999), No. 4, 423--470 (with L. A. Sakhnovich) pdf file
• A boundary Nevanlinna-Pick problem for a class of analytic matrix-valued functions in the unit ball, Linear Algebra Appl. 346 (2002), 239-260. pdf file
• A tangential interpolation problem on the distinguished boundary of the polydisk for the Schur-Agler class. J. Math. Anal. Appl. 273 (2002), no. 2, 328--348 (with J. A. Ball). pdf file
• Interpolation for multipliers on reproducing kernel Hilbert spaces. Proc. Amer. Math. Soc. 131 (2003), no. 5, 1373--1383. pdf file
• A bitangential interpolation problem on the closed unit ball for multipliers of the Arveson space, Integral Equations Operator Theory 46 (2003), 125-164 (with J. A. Ball) pdf file
• Positive extension problems for a class of structured matrices, Linear Algebra Appl. 381 (2004), 165-195 (with P. A. Smith). pdf file
• Nevanlinna-Pick interpolation: Pick matrices have bounded number of negative eigenvalues, Proc. Amer. Math. Soc. 132 (2004), 769-780 (with A. Kheifets; L. Rodman) pdf file
• On Caratheodory--Fejer problem for generalized Schur functions, Integral Equations Operator Theory 50 (2004), no.1, 9-41. pdf file
• Realization and interpolation for Schur-Agler-class functions on domains with matrix polynomial defining function in C^n, J. Funct. Anal. 213 (2004), 45--87 (with J. A. Ball). pdf file
• Boundary interpolation for contractive-valued functions on circular domains in C^n, Operator Theory: Advances and Applications 149 (2004), 107--132 (with J. A. Ball). pdf file