Publications

For recent papers (since 2014 or so), links point to the paper's page on arxiv.org; for older papers the links point directly to pdf files. As always, the versions here may differ from the final published versions.

Preprints

• Determinants of random unitary pencils (with George Roman)

• A note on homotopies of rational matrix inner functions

To appear

Published

2024

• Positivity conditions on the annulus via the double-layer potential kernel (with G. Tsikalas), Studia Math., 278 (2024), 233-265.

• An optimal approximation problem for free polynomials (with P. Arora, M. Augat, and M. Sargent),
  Proc. Amer. Math. Soc., 152 (2024), 455-470.

• The kernel perspective on dynamic mode decomposition (with E. Gonzalez, M. Abudia, R. Kamalapurkar, and J. Rosenfeld)
  Transactions on Machine Learning Research, September 2024

• (book chapter) Noncommutative inner-outer factorizations (with R.T.W. Martin and E. Shamovich)
  In: Alpay, D., Sabadini, I., Colombo, F. (eds) Operator Theory. Springer, Basel. (2024)

2023

• (book chapter) A brief introduction to noncommutative function theory.
  In: Mashreghi, J. (eds) Lectures on Analytic Function Spaces and their Applications. Fields Institute Monographs, vol 39. Springer, Cham. (2023).

• Sub-Hardy Hilbert spaces in the non-commutative row ball (with R.T.W. Martin),
  in Binder, I., Kinzebulatov, D., Mashreghi, J. (eds) Function Spaces, Theory and Applications. Fields Institute Communications, vol 87. Springer, Cham., (2023).

• Denjoy-Wolff points on the bidisk via models (with G. Tsikalas),
  Integral Equations and Operator Theory, (2023) 95:30, 42pp.

• Non-commutative rational Clark measures (with R.T.W. Martin and E. Shamovich),
  Canadian J. Math., 75 (2023) no. 5, 1393-1445.

• A non-commutative F&M Riesz Theorem (with R.T.W. Martin and E. Timko),
  Journal of Operator Theory, 90 (2023) no. 2, 569-604.

2022

• Noncommutative partially convex rational functions (with I. Klep, M. Mancuso, S. McCullough, and J.E. Pascoe),
  Revista Matematica Iberoamericana, 38 (2022), no. 3, 731–759.

• Unbounded multipliers of complete Pick spaces (with R.T.W. Martin),
  Integral Equations and Operator Theory, 94 (2022), paper no. 14, 28 pages.

• Fatou’s Theorem for non-commutative measures (with R.T.W. Martin),
  Advances in Mathematics, 400 (2022), Paper No. 108293, 53 pp..

• Lebesgue decomposition of non-commutative measures (with R.T.W. Martin),
  International Mathematics Research Notices, 2022, no. 4, 2968–3030.

2021

• Non-commutative rational functions in the full Fock space (with R.T.W. Martin and E. Shamovich),
  Trans. Amer. Math. Soc., 374 (2021), no. 9, 6727–6749.

• Blaschke-Singular-Outer factorization of free non-commutative functions (with R.T.W. Martin and E. Shamovich),
  Advances in Mathematics, 384 (2021), Paper No. 107720, 42 pp.

• Szegő and Widom theorems for finite codimensional subalgebras of a class of uniform algebras (with D. Pfeffer),
  Complex Anal. Oper. Theory 15 (2021), no. 5, Paper No. 83, 37 pp.

• Noncommutative partial convexity via Γ-convexity (with I. Klep, M. Mancuso, S. McCullough, and J.E. Pascoe),
  Journal of Geometric Analysis, 31 (2021), 3137-3160.

• The Smirnov classes for the Fock space and complete Pick spaces (with R.T.W. Martin),
  Indiana Univ. Math. J., 70 (2021) no. 1, 269-284.

2020

• Effective noncommutative Nevanlinna-Pick interpolation in the row ball, and applications (with M. Augat and J.E. Pascoe),
  Journal of Mathematical Analysis and Applications, 492 (2020), no. 2, 21 pages.

• Column extreme multipliers of the Free Hardy space (with R.T.W. Martin)
  Jour. London Math.Soc., 101 (2020) no.2, 457-489.

pre-2020

• Operators affiliated to the free shift on the free Hardy space (with R.T.W. Martin)
  Journal of Functional Analysis, 277 (2019) Issue 12, Article 108285.

• Factorization in weak products of complete Pick spaces (with R.T.W. Martin)
  Bull. London Math. Soc. 51 (2019), no. 2, 223-229.

• Extremal multipliers of the Drury-Arveson space (with R.T.W. Martin)
  Proc. Amer. Math. Soc. 146 (2018), 4293-4306 .

• Non-commutative Clark measures for the free and abelian Toeplitz algebras (with R.T.W. Martin)
  Journal of Mathematical Analysis and Applications 456, Issue 2 (2017), Pages 1062-1100

• Aleksandrov-Clark theory for Drury-Arveson space (with R.T.W. Martin),
  Integral Equations and Operator Theory, (2018), in press

• Dilations and constrained algebras (with M. Dritschel and S. McCullough)
  Operators and Matrices, 10 No. 4 (2016), 829–861

• Does every contractive analytic function in a polydisk have a dissipative n-dimensional scattering realiztion?
  Complex Analysis and Operator Theory 9, Issue 4 (2015) 821–825

• Clark theory in the Drury-Arveson space
  Journal of Functional Analysis, 266, Issue 6, (2014), 3855–3893

• Universal commutative operator algebras and transfer function realizations of polynomials,
  Integral Equations and Operator Theory, 73 No. 3 (2012), 305–329.

• Nevanlinna-Pick interpolation on distinguished varieties in the bidisk (with G. Knese and S. McCullough),
  Journal of Functional Analysis, 262 (2012), 3812–3838.

• Valiron’s theorem in the unit ball and spectra of composition operators,
  Journal of Mathematical Analysis and Applications, 368 (2010), 482–490.

• Composition operators on Hardy spaces of a half plane (with S. Elliott),
  Bull. London Math. Soc., 44 No. 3 (2012), 489-495.

• Agler interpolation families of kernels (with G. Knese and S. McCullough),
  Operators and Matrices, 3 No. 4 (2009), 571–587.

• Operator-valued Herglotz kernels and functions of positive real part on the ball,
  Complex Analysis and Operator Theory, 4 No. 2 (2010), 301–317.

• Norms and spectral radii of linear fractional composition operators on the ball,
  Journal of Functional Analysis, 254 No. 9 (2008), 2387–2400.

• The Fredholm index for elements of Toeplitz-composition C*-algebras,
  Integral Equations and Operator Theory, 58 No. 3 (2007), 341-362.

• Reporducing kernels, de Branges-Rovnyak spaces, and norms of weighted composition operators,
  Proc. Amer. Math. Soc., 135 No. 11 (2007), 3669-3675.

• C*-algebras generated by groups of composition operators,
  Indiana Univ. Math. J., 56 No. 6 (2007), 3171–3192.

• Invariant subspaces for a class of complete Pick kernels,
  Proc. Amer. Math. Soc., 133 No. 12 (2005), 3589-3596.

• Partially isometric dilations of noncommuting N-tuples of operators (with D. Kribs),
  Proc. Amer. Math. Soc., 133 No. 1 (2005), 213-222.

• Ideals in free semigroupoid algebras from directed graphs (with D. Kribs),
  Journal of Operator Theory, 53 No. 2 (2005), 273-302.