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.
46. With Ching-Wei Ho, The Brown measure of the sum of a self-adjoint element and an imaginary multiple of a semicircular element, preprint arXiv:2006.07168 [math.PR]
45. PDE methods in random matrix theory, submitted to Springer volume, "Harmonic Analysis and Applications." This is an expository article based on the material in Publication 44 and provides a gentle introduction to the concept of Brown measure as well as the PDE methods used to compute the Brown measure of the free multiplicative Brownian motion. Preprint arXiv:1910.09274 [math.PR] .
44. With B. Driver and T. Kemp, 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. With B. Driver and T. Kemp, The complex-time Segal-Bargmann transform, *J. Funct. Anal.* **278** (2020), Article 10830 (42 pages)
42. With T. Kemp, Brown measure support and the free multiplicative Brownian motion, *Advances in Math. ***355** (2019), Article106771 (36 pages)
41. The eigenvalue process for Brownian motion in *U(N)*, unpublished notes, eigenvalue.pdf
40. 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.
39. 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.
38. 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).
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 |