Note: the versions here may differ from the final published versions.

Preprints

• Positivity conditions on the annulus via the double-layer potential kernel (with G. Tsikalas), preprint.
• A note on homotopies of rational matrix inner functions, preprint.

Accepted/In Press

Published

• An Optimal Approximation Problem For Free Polynomials (with P. Arora, M. Augat, and M. Sargent), Proc. Amer. Math. Soc., 152 (2024), 455-470.
• (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.
• 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.
• 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.
• 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.
•  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.