Staff Profile

Roles and Responsibilities

Research in mathematical analysis

Qualifications

M.A., D.Phil. (Oxon) 

Research Interests

Mathematical analysis, particularly operators on Hilbert space; complex analysis; H infinity control.

• Articles

  • Agler J, Lykova ZA, Young NJ. Function theory in the bfd-norm on an elliptical region. Journal of Mathematical Analysis and Applications 2025, 541(2), 128732.
  • Agler J, Lykova ZA, Young NJ. On the operators with numerical range in an ellipse. Journal of Functional Analysis 2024, 287(8), 110556.
  • Agler J, Lykova ZA, Young NJ. A Hilbert space approach to singularities of functions. Journal of Functional Analysis 2023, 284(6), 109826.
  • Agler J, Lykova ZA, Young NJ. Nonuniqueness of Carathéodory extremal functions on the symmetrized bidisc. Analysis Mathematica 2022, 48, 287-306.
  • Agler J, Lykova ZA, Young NJ. Intrinsic Directions, Orthogonality and Distinguished Geodesics in the Symmetrized Bidisc. The Journal of Geometric Analysis 2021, 31, 8202-8237.
  • Chiotis D, Lykova ZA, Young NJ. Exterior products of operators and superoptimal analytic approximation. Transactions of the London Mathematical Society 2021, 8(1), 299-412.
  • Chiotis D, Lykova ZA, Young NJ. Exterior powers and pointwise creation operators. Complex Analysis and Operator Theory 2021, 15, 29.
  • Clairon Q, Henderson R, Young NJ, Taylor CJ, Wilson ED. Adaptive treatment and robust control. Biometrics 2021, 77(1), 223-236.
  • Agler J, Lykova Z, Young N. Geodesics, retracts, and the norm-preserving extension property in the symmetrized bidisc. Memoirs of the American Mathematical Society 2019, 258(1242), 1-108.
  • Agler J, Lykova ZA, Young NJ. Characterizations of some domains via Carathéodory extremals. Journal of Geometric Analysis 2019, 29(4), 3039–3054.
  • Agler J, McCarthy JE, Young NJ. Calcular algebras. Mathematical Proceedings of the Royal Irish Academy 2019, 119A(2), 65-75.
  • Agler J, Lykova ZA, Young NJ. A geometric characterization of the symmetrized bidisc. Journal of Mathematical Analysis and Applications 2019, 473(2), 1377-1413.
  • Agler J, McCarthy JE, Young NJ. Non-commutative manifolds, the free square root and symmetric functions in two non-commuting variables. Transactions of the London Mathematical Society 2018, 5(1), 132–183.
  • Agler J, Lykova ZA, Young NJ. Algebraic and geometric aspects of rational Γ-inner functions. Advances in Mathematics 2018, 328, 133-159.
  • Agler J, Young NJ. Realization of functions on the symmetrized bidisc. Journal of Mathematical Analysis and Applications 2017, 453(1), 227-240.
  • Agler J, Lykova ZA, Young NJ. Finite Blaschke products and the construction of rational $\Gamma$-inner functions. Journal of Mathematical Analysis and Applications 2017, 447(2), 1163–1196.
  • Brown DC, Lykova ZA, Young NJ. A rich structure related to the construction of analytic matrix functions. Journal of Functional Analysis 2017, 272(4), 1704-1754.
  • Agler J, Tully-Doyle R, Young NJ. Nevanlinna representations in several variables. Journal of Functional Analysis 2016, 270(8), 3000-3046.
  • Agler J, Lykova Z, Young NJ. The complex geometry of a domain related to μ-synthesis. Journal of Mathematical Analysis and Applications 2015, 422(1), 508-543.
  • Agler J, Lykova ZA, Young NJ. 3-extremal holomorphic maps and the symmetrised bidisc. Journal of Geometric Analysis 2015, 25(3), 2060-2102.
  • Agler J, Young NJ. Symmetric functions of two noncommuting variables. Journal of Functional Analysis 2014, 266(9), 5709-5732.
  • Agler J, McCarthy JE, Young NJ. Corrigendum to: Operator monotone functions and Löwner functions of several variables. Annals of Mathematics 2014, 180(1), 403-405.
  • Agler J, McCarthy JE, Young NJ. On the representation of holomorphic functions on polyhedra. Michigan Mathematical Journal 2013, 62(4), 675-689.
  • Agler J, Lykova ZA, Young NJ. Extremal holomorphic maps and the symmetrized bidisc. Proceedings of the London Mathematical Society 2013, 106(4), 781-818.
  • Agler J, Lykova ZA, Young NJ. A Case of $\mu$-Synthesis as a Quadratic Semidefinite Program. SIAM Journal on Control and Optimization 2013, 51(3), 2472-2508.
  • Agler J, Lykova ZA, Young NJ. Pseudo-Taylor expansions and the Carathéodory-Fejér problem. Journal of Mathematical Analysis and Applications 2012, 386(1), 308-318.
  • Agler J, McCathy JE, Young NJ. Operator monotone functions and Löwner functions of several variables. Annals of Mathematics 2012, 176(3), 1783-1826.
  • Agler J, Tully-Doyle R, Young NJ. Boundary behavior of analytic functions of two variables via generalized models. Indagationes Mathematicae 2012, 23(4), 995-1027.
  • Agler J, McCarthy JE, Young NJ. A Carathéodory theorem for the bidisk via Hilbert space methods. Mathematische Annalen 2012, 352(3), 581-624.
  • Agler J, Lykova ZA, Young NJ. The boundary Carathéodory–Fejér interpolation problem. Journal of Mathematical Analysis and Applications 2011, 382(2), 645-662.
  • Agler J, McCarthy JE, Young NJ. Facial behaviour of analytic functions on the bidisk. Bulletin of the London Mathematical Society 2011, 43(3), 478-494.
  • Agler J, Young NJ. Boundary Nevanlinna-Pick interpolation via reduction and augmentation. Mathematische Zeitschrift 2011, 268(3-4), 791-817.
  • Agler J, Young NJ. The magic functions and automorphisms of a domain. Complex Analysis and Operator Theory 2008, 2(3), 383-404.
  • Young NJ. The automorphism group of the tetrablock. Journal of the London Mathematical Society 2008, 77(3), 757-770.
  • Abouhajar AA, White MC, Young NJ. A Schwarz Lemma for a domain related to μ-synthesis. Journal of Geometric Analysis 2007, 17(4), 717-750.
  • Huang H-N, Marcantognini SAM, Young NJ. The spectral Carathéodory-Fejér problem. Integral Equations and Operator Theory 2006, 56(2), 229-256.
  • Agler J, Young NJ. The complex geodesics of the symmetrised bidisc. Int. J. Math 2006, 17(4), 375-391.
  • Huang HN, Marcantognini SAM, Young NJ. Chain rules for higher derivatives. Mathematical Intelligencer 2006, 28(2), 61-69.
  • Agler J, Young NJ. The two-by-two spectral Nevanlinna-Pick problem. Transactions of the American Mathematical Society 2004, 356, 573-585.
  • Agler J, Young NJ. The hyperbolic geometry of the symmetrized bidisc. Journal of Geometric Analysis 2004, 14(3), 375-403.
  • Agler J, Young NJ. A model theory for Γ-contractions. Journal of Operator Theory 2003, 49(1), 45-60.
  • Agler J, Young N. A model theory for $\Gamma$-contractions. Journal of Operator Theory 2003, 49(1), 45-60.
  • Ogle D, Young NJ. The Parrott problem for singular values. Operator Theory 2001, 124, 481-503.
  • Agler J, Young NJ. A Schwarz Lemma for the symmetrized bidisc. Bulletin of the London Mathematical Society 2001, 33(2), 175-186.
  • Agler J, Young NJ. The two-point spectral Nevanlinna-Pick problem. Integral Equations and Operator Theory 2000, 37(4), 375-385.
  • Ball JA, Young NJ. Problems on the realization of functions. Fields Institute Communications 2000, 25, 179-185.
  • Agler J, Young NJ. Operators having the symmetrized bidisc as a spectral set. Proceedings of the Edinburgh Mathematical Society 2000, 43(1), 195-210.
  • Agler J, Young NJ. A converse to a theorem of Adamyan, Arov and Krein. Journal of the American Mathematical Society 1999, 12(2), 305-333.
  • Agler J, Young NJ. A Commutant Lifting Theorem for a Domain in ℂ2 and Spectral Interpolation. Journal of Functional Analysis 1999, 161(2), 452-477.
  • Young NJ, Peller VV. Continuity properties of best analytic approximation. J. für die Reine und Angewandte Mathematik 1997, 483, 1-22.
  • Young NJ, Peller, VV. Superoptimal analytic approximations of matrix functions. J. Functional Analysis 1994, 120, 300-343.
  • Young NJ. An Introduction to Hilbert Space. Cambridge University Press 1988, 240.
  • Young NJ. The Nevanlinna-Pick problem for matrix-valued functions. J. Operator Theory 1986, 15, 239-265.
  • Young NJ. Orbits of the unit sphere of $L(H,K)$ under symplectic transformations. J. Operator Theory 1984, 11, 171-191.

• Authored Book

  • Agler J, McCarthy JE, Young NJ. Operator Analysis: Hilbert Space Methods in Complex Analysis. Cambridge: Cambridge University Press, 2020.

• Book Chapters

  • Lykova ZA, Young NJ, Ajibo AE. Analytic interpolation into the tetrablock and a μ-synthesis problem. In: Bolotnikov V; ter Horst S; Ran ACM; Vinnikov V, ed. Interpolation and Realization Theory with Applications to Control Theory. Basel: Springer, 2019, pp.235-247.
  • Agler J, Lykova ZA, Young NJ. Carathéodory extremal functions on the symmetrized bidisc. In: Bart, H; ter Horst, S; Ran, ACM; Woerdeman, HJ, ed. Operator Theory, Analysis and the State Space Approach. Birkhäuser Basel: Birkhaeuser Science, 2018, pp.1-21.
  • Young NJ. Some analysable instances of mu-synthesis. In: Dym, H., de Oliveira, M., Putinar, M, ed. Mathematical Methods in Systems, Optimization, and Control. Basel: Birkhäuser, 2012, pp.349-366.
  • Agler J, Yeh FB, Young NJ. Realization of functions into the symmetrised bidisc. In: Alpay, D, ed. Reproducing Kernel Spaces and Applications. Basel; Boston: Birkhauser, 2003, pp.1-37.