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For information about my books, Lie Groups, Lie Algebras, and Representations, and Quantum Theory for Mathematicians, both published by Springer, see the "Books" link at left.

Please e-mail me at bhall@nd.edu for reprints of any published article listed below.

 

44. The Brown measure of the free multiplicative Brownian motion, preprint arXiv:1903.11015 [math.PR]

A Mathematica notebook containing all the plots and simulations appearing in the above paper is available at this link: https://www.notebookarchive.org/id/2019-05-bjnnq2h . There you can either view the notebook directly on the web or download the file (52 MB!) so that you can run your own simulations. Please note that even when viewing on the web, it will take a few minutes for the file to load.

43. Brown measure support and the free multiplicative Brownian motion, preprint arXiv:1810.00153 [math.FA]

42. The eigenvalue process for Brownian motion in U(N), unpublished notes, eigenvalue.pdf

41. With Benjamin Lewis, A unitary "quantization commutes with reduction" map for the adjoint action of a compact Lie group, Quarterly Journal of Math. 69 (2018), 1387-1421.

 

40. Coherent states for compact Lie groups and their large-N limits, in "Coherent states and their applications: a contemporary panorama" (J.-P. Antoine, F. Bagarello, and J.-P. Gazeau, eds.), Springer, 2018.

39. The large-N limit for two-dimensional Yang-Mills theory, Comm. Math. Phys. 363 (2018), 789-828. Available from the journal's website here (read only).

38. With B. Driver and T. Kemp, The complex-time Segal-Bargmann transform, arXiv:1610.00090 [math.FA]

 

37. With B. Driver, F. Gabriel, and T. Kemp, The Makeenko-Migdal equation for Yang-Mills theory on compact surfaces, Comm. Math. Phys. 352 (2017), 967-978. Available from the journal's website here (read only)

 

36. With B. Driver and T. Kemp, Three proofs of the Makeenko-Migdal equation for Yang-Mills theory on the plane, Comm. Math. Phys. 351 (2017), 741-774. Available from the journal's website here (read only).

 

35. With J. Mitchell, The Segal-Bargmann transform for odd-dimensional hyperbolic spaces, Mathematics 3 (2015), 758-780. Open access.

34. The Segal-Bargmann transform for unitary groups in the large-N limit, expository article on the material in joint paper (Ref. 32) with Driver and Kemp. Large-N

33. With M. Cecil, Dimension-independent estimates for heat operators and harmonic functions, Potential Anal. 40 (2014), 363–389.

32. With B. K. Driver and T. Kemp, The large-N limit of the Segal-Bargmann transform on U(N), J. Funct. Anal. 265 (2013), 2585-2644.

31. With W. Kirwin, Complex structures adapted to magnetic flows, J. Geom. Phys. 90 (2015), 111-131.

30. With J. Mitchell, Coherent states for a particle on a 2-sphere with a magnetic field, J. Physics A, 45 (2012), 18 pages. (Special issue on coherent states). JPhysA.pdf

29. With K. Chailuek, Toeplitz operators on generalized Bergman spaces. Integral Eq. Operator Theory 66 (2010), 53-77.

28. With W. Kirwin, Adapted complex structures and the geodesic flow. Mathematische Annalen 350 (2011), 455-474. MathAnn350

27. Berezin-Toeplitz quantization on Lie groups, J. Funct. Anal. 255 (2008), 2488-2506 (Special issue in honor of Paul Malliavin). Jfa255

26. Leonard Gross's work in infinite-dimensional analysis and heat kernel analysis, Comm. on Stochastic Analysis (special volume in honor of Leonard Gross), 2 (2008), 1-9. GrossCosa.pdf

25. The heat operator in infinite dimensions, in "Infinite Dimensional Analysis in Honor of H.-H. Kuo," edited by A. N. Sengupta and P. Sundar, World Scientific 2008, pp. 161-174.

24. With J. Mitchell, The Segal-Bargmann transform for compact quotients of symmetric spaces of the complex type. Taiwanese J. Math. 16 (2012), 13-45. Link to TJM Volume 16

23. With J. Mitchell, Isometry theorem for the Segal-Bargmann transform on a noncompact symmetric space of the complex type, J. Functional Analysis 254 (2008), 1575-1600. jfa254

22. With W. Kirwin, Unitarity in "quantization commutes with reduction," Comm. Math. Phys. 275 (2007), 401-442. cmp275

21. With J. J. Mitchell, The Segal-Bargmann transform for noncompact symmetric spaces of the complex type, J. Functional Analysis 227 (2005), 338-371. jfa227.pdf

20. The range of the heat operator, in "The Ubiquitous Heat Kernel," edited by

Jay Jorgensen and Lynne Walling, AMS 2006, pp. 203-231. range.pdf

19. With W. Lewkeeratiyutkul, Holomorphic Sobolev spaces and the generalized Segal-Bargmann transform, J. Functional Analysis 217 (2004), 192-220. jfa217.pdf

18. With M. B. Stenzel, Sharp bounds for the heat kernel on certain symmetric spaces of non-compact type. In, "Finite and Infinite Dimensional Analysis in Honor of Leonard Gross" (H.-H. Kuo and A. N. Sengupta, Eds.) 117-135, Contemp. Math. 317, Amer. Math. Soc., 2003. gross2.pdf

17. The Segal-Bargmann transform and the Gross ergodicity theorem. In, "Finite and Infinite Dimensional Analysis in Honor of Leonard Gross" (H.-H. Kuo and A. N. Sengupta, Eds.), 99-116, Contemp. Math. 317, Amer. Math. Soc., 2003. gross1.pdf

16. With J. J. Mitchell, The large radius limit for coherent states on spheres. In, "Mathematical Results in Quantum Mechanics" (R. Weder, et al., Eds.), 155-162, Contemp. Math. 307, Amer. Math. Soc., 2002. qmath.pdf

15. Geometric quantization and the generalized Segal-Bargmann transform for Lie groups of compact type, Comm. Math. Phys. 226 (2002), 233-268.cmp226.pdf

14. With J. J. Mitchell, Coherent states on spheres, J. Math. Phys. 43 (2002), 1211-1236. jmp43.pdf

13. Bounds on the Segal-Bargmann transform of Lp functions, J. Fourier Analysis Applications 7 (2001), 553-569. jfaa7.pdf

12. Coherent states and the quantization of (1+1)-dimensional Yang-Mills theory, Rev. Math. Phys. 13 (2001), 1281--1305. rmp13

11. Harmonic analysis with respect to heat kernel measure, Bull. Amer. Math. Soc. (N.S.) 38 (2001), 43-78. bull38.pdf

10. With B. K. Driver, The energy representation has no non-zero fixed vectors. In, "Stochastic Processes, Physics and Geometry: New Interplays, II" (Leipzig, 1999), 143-155, CMS Conf. Proc., 29, Amer. Math. Soc., Providence, RI, 2000.

9. Holomorphic methods in analysis and mathematical physics. In, "First Summer School in Analysis and Mathematical Physics" (S. Pérez-Esteva and C. Villegas-Blas, Eds.), 1-59, Contemp. Math. 260, Amer. Math. Soc., 2000. holomorphic_methods.pdf

8. With S. Albeverio and A. N. Sengupta, The Segal-Bargmann transform for two-dimensional Euclidean quantum Yang-Mills, Infin. Dimens. Anal. Quantum Probab. Relat. Top. 2 (1999), 27-49. idaqp2.pdf

7. A new form of the Segal-Bargmann transform for Lie groups of compact type, Canad. J. Math. 51 (1999), 816-834.

6. With B. K. Driver, Yang-Mills theory and the Segal-Bargmann transform, Comm. Math. Phys. 201 (1999), 249-290. cmp201.pdf

5. With A. N. Sengpupta, The Segal-Bargmann transform for path-groups, J. Functional. Analysis 152 (1998), 220-254. jfa152.pdf

4. Quantum mechanics in phase space. In, "Perspectives on Quantization" (L. Coburn and M. Rieffel, Eds.), 47-62, Contemp. Math., 214, Amer. Math. Soc., Providence, RI, 1998

3. Phase space bounds for quantum mechanics on a compact Lie group, Comm. Math. Phys. 184 (1997), 233-250. cmp184.pdf

2. The inverse Segal-Bargmann transform for compact Lie groups, J. Functional Analysis 143 (1997), 98-116. jfa143.pdf

1. The Segal-Bargmann "coherent state" transform for compact Lie groups, J. Functional Analysis 122 (1994), 103-151. jfa122.pdf

   

 

 

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