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.

2026

• Determinants of random unitary pencils
  (with G. Roman)
  Journal of Functional Analysis 291 Issue 6 (2026) Paper no. 111555, 60 pages.
• A note on homotopies of rational matrix inner functions
  Proc. Amer. Math. Soc. 154 (2026) 1639-1643

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) 1062–1100.
• Aleksandrov-Clark theory for Drury-Arveson space
  (with R.T.W. Martin)
  Integral Equations and Operator Theory (2018).
• 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 realization?
  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.
• Reproducing 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.