44. M.L. Augat, R.T.W. Martin and E. Shamovich. Operator realizations of non-commutative analytic functions. Forum of Mathematics, ∑ , 2025.
43. R.T.W. Martin and E.J. Timko. Absolute continuity in the reproducing kernel sense. Canadian Mathematical Bulletin, 2025.
42. R.T.W. Martin. On log-integrability of Radon-Nikodym derivatives. "Operator Theory" (Springer reference), 2024.
41. M.T. Jury, R.T.W. Martin and E. Shamovich. Non-commutative inner-outer factorizations. "Operator Theory" (Springer reference), 2024.
40. J. Bal, R.T.W. Martin and F. Naderi. A reproducing kernel approach to Lebesgue decomposition. Canadian Journal of Mathematics, 2024.
39. R.T.W. Martin and E. Shamovich. Rational Cuntz states peak on the free disk algebra. arXiv:2307.00508. Bulletin of the London Mathematical Society, 2024.
38. M.T. Jury and R.T.W. Martin. Sub-Hardy Hilbert spaces in the non-commutative unit row-ball. arXiv:2204.05016. Function Spaces, Theory and Applications, Fields Institute Communications, 2024.
37. M.T. Jury, R.T.W. Martin and E.J. Timko. A non-commutative F.&M. Riesz theorem. arXiv:2201.07393, Journal of Operator Theory, 2022.
36. M.T. Jury, R.T.W. Martin and E. Shamovich. Non-commutative rational Clark measures. arXiv:2201:08045, Canadian Journal of Mathematics, 2022.
35. R.T.W. Martin. On unitary equivalence to a self-adjoint or doubly--positive Hankel operator. Concrete Operators, 2022.
34. M. Bush, C. Liaw and R.T.W. Martin. Spectral measures for derivative powers via matrix-valued Clark theory. Journal of Mathematical Analysis and Applications, 2022.
33. M.T. Jury and R.T.W. Martin. Unbounded multipliers of complete Pick spaces. Integral Equations and Operator Theory, 2022.
32. M.T. Jury and R.T.W. Martin. Fatou's theorem for non-commutative measures. Advances in Mathematics, 2022.
- We extend the Radon-Nikodym derivative formula of Fatou’s Theorem to the setting of non-commutative measures and their Poisson Transforms.
31. M.T. Jury, R.T.W. Martin and E. Shamovich. Blaschke-Singular-Outer Factorization of free non-commutative functions. Advances in Mathematics, 2021.
- We extend the classical Blaschke--Singular--Outer factorization of analytic functions in the complex unit disk to the setting of the full Fock space, identified as the non-commutative (NC) Hardy space of square--summable power series in several NC variables.
30. M.T. Jury, R.T.W. Martin and E. Shamovich. Non-commutative rational functions in the full Fock space. Transactions of the American Mathematical Society, 2021.
29. R. Clouâtre, R.T.W. Martin and E.J. Timko. Analytic functionals for the non-commutative disc algebra. Journal of Functional Analysis, 2021.
28. M.T. Jury and R.T.W. Martin. Lebesgue decomposition of non-commutative measures. International Mathematics Research Notices, 2022.
- Three classical approaches to Lebesgue Decomposition Theory are extended to the setting of non-commutative measures, and we prove that the sets of absolutely continuous and singular NC measures are positive cones.
27. C. Liaw, R.T.W. Martin and S. Treil. Matrix-valued Aleksandrov-Clark measures and Carathéodory angular derivatives. Journal of Functional Analysis, 2020.
26. R.T.W. Martin and E. Shamovich. A de Branges-Beurling theorem for the full Fock space. Journal of Mathematical Analysis and Applications, 2020.
25. M.T. Jury and R.T.W. Martin. Operators affiliated to the free shift on the free Hardy space. Journal of Functional Analysis, 2019.
24. M.T. Jury and R.T.W. Martin. Column extreme multipliers of the free Hardy space. Journal of the London Mathematical Society, 2019.
- Several equivalent classical characterizations of extreme points of the Schur class of contractive analytic functions on the complex unit disk are extended to the non-commutative, multi-variable setting.
23. R.T.W. Martin and A. Ramanantoanina. A Gleason solution model for row contractions. Operator Theory: Advances and Applications 272:249-305, 2019.
22. M.T. Jury and R.T.W Martin. The Smirnov classes for the Drury-Arveson and Fock spaces. Indiana University Mathematics Journal, 2021.
21. M.T. Jury and R.T.W. Martin. Aleksandrov-Clark theory for Drury-Arveson space. Integral Equations and Operator Theory. 90, 2018.
20. M.T. Jury and R.T.W. Martin. Extremal multipliers of the Drury-Arveson space. Proceedings of the American Mathematical Society. 146:4293-4306, 2018.
19. M.T. Jury and R.T.W. Martin. Factorization in weak products of complete Pick spaces. Bulletin of the London Mathematical Society. 51:223-229, 2019.
18. J. Levick and R.T.W. Martin. Matrix N-dilations of quantum channels. Operators and Matrices. 12:977-995, 2018.
17. M.T. Jury and R.T.W. Martin. Noncommutative Clark measures for the free and abelian Toeplitz algebras. Journal of Mathematical Analysis and Applications. 456:1062-1100, 2017.
- The seminal concept of Aleksandrov-Clark measure for a contractive analytic function on the complex unit disk is extended to the several-variable and non-commutative settings.
16. R.T.W. Martin and A. Kempf. Function spaces obeying a time-varying bandlimit. J. Math. Anal. Appl. 458:1597-1638, 2018.
15. A. Chatwin-Davies, A. Kempf and R.T.W. Martin. Natural covariant Planck scale cutoffs and the cosmic microwave background spectrum. Physical Review Letters. 119:031301, 2017.
14. S.R. Garcia, R.T.W. Martin and W.T. Ross. Partial orders on partial isometries. Journal of Operator Theory. 75:409-442, 2016.
13. R.T.W Martin. Extensions of symmetric operators I: The inner characteristic function case. Concrete Operators. 2:53-97, 2015.
12. R.T.W. Martin. Near invariance and symmetric operators. Oper. Matrices. 8:513-528, 2014.
11. A. Aleman, R.T.W. Martin and W.T. Ross. On a theorem of Livsic. J. Funct. Anal. 264:999-1048, 2013.
10. A. Kempf, A. Chatwin-Davies and R.T.W. Martin. A fully covariant information-theoretic ultraviolet cutoff for scalar fields in expanding Friedmann Robertson Walker spacetimes. J. Math. Phys. 54:022301, 2013.
9. R.T.W. Martin. Unitary perturbations of compressed N-dimensional shifts. Compl. Anal. Oper. Theory. 7:765-799, 2013.
8. R.T.W. Martin. Semigroups of partial isometries and symmetric operators. Integral Equations Operator Theory. 70:205-226, 2011.
7. R.T.W. Martin. Representation of symmetric operators with deficiency indices (1,1) in de Branges space. Compl. Anal. Oper. Theory. 5:545-577, 2011.
6. R.T.W. Martin. Symmetric operators and reproducing kernel Hilbert spaces. Compl. Anal. Oper. Theory. 4: 845-880, 2010.
5. R.T.W. Martin. Characterization of the unbounded bicommutant of C0(N) contractions. Oper. Matrices. 3:589-598, 2009.
4. R.T.W. Martin and A. Kempf. Quantum uncertainty and the spectra of symmetric operators. Acta Appl. Math. 106:349-358, 2009.
3. R.T.W. Martin and A. Kempf. Approximation of bandlimited functions on a non-compact manifold by bandlimited functions on submanifolds. Sampl. Theory Signal Image Process. 7:282-292, 2008.
2. A. Kempf and R.T.W. Martin. Information theory, spectral geometry and quantum gravity. Phys. Rev. Lett. 100:021304, 2008.
1. R.T.W. Martin. Approximation of A-bandlimited functions by A-bandlimited trigonometric polynomials. Sampl. Theory Signal Image Process. 6:273-296, 2007.
Here is a proof of the existence of NC pluri-harmonic conjugates of NC pluri-harmonic functions. (This appears in the preprint ` Free potential functions' of M.L. Augat.)