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Staff Profile

Dr Michael Dritschel

Reader in Pure Mathematics

  • Email: michael.dritschel@ncl.ac.uk
  • Telephone: +44 (0) 191 208 7229
  • Fax: +44 (0) 191 208 8020
  • Personal Website:
  • Address: School of Mathematics, Statistics and Physics
    Herschel Building
    Â鶹´«Ã½
    Â鶹´«Ã½ upon Tyne
    NE1 7RU
    UK
Research

Research Interests

These are, broadly speaking, operator theory, operator algebras, complex function theory, and the interplay between these areas. My most recent work is a Fejer-Riesz type factorization theorem for non-negative operator valued trigonometric polynomials in two variables.  I've also co-authored a paper with my student Batzorig Undrakh on the rational dilation problem for spectral sets contained in a broad class of distinguished varieties, vastly extending work done both with another former student, James Pickering, and with Scott McCullough and Michael Jury.

Publications
  • Dritschel MA. Factoring non-negative operator valued trigonometric polynomials in two variables. 2019. Available at: https://arxiv.org/pdf/1811.06005. Submitted.
  • Dritschel MA, Undrakh B. . Journal of Mathematical Analysis and Applications 2018, 467(1), 95-131.
  • Dritschel MA, Estevez D, Yakubovich D. . Journal of Mathematical Analysis and Applications 2018, 463(1), 345-364.
  • Dritschel MA, Estévez D, Yakubovich D. . Journal of Functional Analysis 2017, 273(3), 984-1019.
  • Dritschel MA, Estévez D, Yakubovich D. . Journal of the London Mathematical Society 2017, 95(2), 414-440.
  • Dritschel MA, Jury MT, McCullough S. . Operators and Matrices 2016, 10(4), 829-861.
  • Dritschel MA. . In: Daniel Alpay, ed. Operator Theory. Basel: Springer, 2015, pp.219-239.
  • Dritschel MA, Bhattacharyya T, ed. . Basel: Birkhauser Basel, 2015.
  • Dritschel MA. Realizations via preorderings with application to the Schur class. 2015. In Preparation.
  • Dritschel MA, Ball JA, ter Elst AFM, Portal P, Potapov D, ed. . Birkhäuser/Springer, Cham, 2014.
  • Dritschel MA, Battacharyya T, Todd CS. Completely Bounded Kernels. Acta Scientiarum Mathematicarum (Szeged) 2013, 79(1-2), 191-217.
  • Dritschel MA, Pickering J. . Transactions of the American Mathematical Society 2012, 364(11), 5589-5604.
  • Dritschel MA, Rovnyak J. . In: Axler, S., Rosenthal, P., Sarason, D, ed. A Glimpse at Hilbert Space Operators: Paul R. Halmos in Memoriam. Basel, Switzerland: Springer, 2010, pp.223-254.
  • Dritschel MA, McCullough S. Test Functions, Kernels, Realizations and Interpolation. In: Bakonyi, M; Gheondea, A; Rovnyak, J, ed. Operator Theory, Structured Matrices, and Dilations: Tiberiu Constantinescu Memorial Volume. Bucharest: American Mathematical Society, 2007.
  • Dritschel MA, Marcantognini S, McCullough S. . Journal fur die Reine und Angewandte Mathematik 2007, (606), 1-40.
  • Dritschel MA, ed. . Basel: Birkhäuser Verlag, 2007.
  • Dritschel MA, Mccullough S. . Journal of the American Mathematical Society 2005, 18(4), 873-918.
  • Dritschel MA, Woerdeman HJ. . Transactions of the American Mathematical Society 2005, 357(11), 4661-4679.
  • Dritschel MA, Mccullough SA. . Journal of Operator Theory 2005, 53(1), 159-167.
  • Dritschel MA. . Integral Equations and Operator Theory 2004, 49(1), 11-42.
  • Dritschel, MA. . In: Alpay, D.; and Vinnikov, V, ed. Operator theory, system theory and related topics. Basel: Birkhäuser, 2001, pp.195-206.
  • Dritschel MA, McCullough S. . Integral Equations and Operator Theory 2000, 36(2), 182-192.
  • Dritschel MA, McCullough S, Woerdeman HJ. . Journal of Operator Theory 1999, 41(2), 321-350.
  • Dritschel Michael A., Woerdeman, Hugo J. Model theory and linear extreme points in the numerical radius unit ball. Memoirs of the American Mathematical Society. No. 615, 3rd of 4 numbers 1997, 129, viii+62.
  • Dritschel MA, Rovnyak J. Operators on indefinite inner product spaces. Fields Institute Monographs no.3, Amer.Math.Soc. Edited by Peter Lancaster 1996, 3, 141-232.
  • Dritschel, Michael A. Compact perturbations of operators on Kre\u\i n spaces. Harmonic analysis and operator theory (Caracas, 1994), Contemp. Math., Amer. Math. Soc., Providence, RI, 1995 1994, 189, 201-211.
  • Cowen, Carl C., Dritschel, Michael A., Penney, Richard C. Norms of Hadamard multipliers. SIAM J. Matrix Anal. Appl 1994, 15(1), 313-320.
  • Dritschel, Michael A. A method for constructing invariant subspaces for some operators on Kre\u\i n spaces. Operator extensions, interpolation of functions and related topics (Timi\c soara, 1992), Oper. Theory Adv. Appl., Birkhäuser, Basel 1993, 61, 85-113.
  • Dritschel, Michael A. The essential uniqueness property for operators on Kre\u\i n spaces. J. Funct. Anal. (Reviewer: Vladimir Derkach) 47B50 1993, 118(1), 198-248.
  • Dritschel, Michael A., Rovnyak, James. Julia operators and complementation in Kre\u\i n spaces. Indiana Univ. Math. J. 40, no. 3, 885--901. (Reviewer: J. Bognár) 46C20 (46E22 47B50) 1991.
  • Dritschel, Michael A., Rovnyak, James. Extension theorems for contraction operators on Kre\u\i n spaces. Extension and interpolation of linear operators and matrix functions, Oper. Theory Adv. Appl., irkhäuser, Basel 1990, 47, 221-305.
  • Dritschel, Michael A. A lifting theorem for bicontractions on Kre\u\i n spaces. J. Funct. Anal. 89 1990, 1, 61-89.