See also the page for my book on Lie groups. Follow the link at left.

27. Berezin-Toeplitz quantization on Lie groups, to appear in J. Functional Analysis. toep_arxiv.pdf

arXiv:0806.3036v1

26. Leonard Gross's work in infinite-dimensional analysis and heat kernel analysis, Comm. on Stochastic Analysis (special volume in honor of Leonard Gross), Vol. 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. Submitted for publication. quotient.pdf

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. Please e-mail me at bhall@nd.edu for a reprint.

22. With W. Kirwin, Unitarity in "quantization commutes with reduction," Comm. Math. Phys. 275 (2007), 401-442. Please e-mail me at bhall@nd.edu for a reprint.

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., Providence, RI, 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., Providence, RI, 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., Providence, RI, 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 Anal. Appl. 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. Review in Math Reviews: MR2002f22034.pdf

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., Providence, RI, 2000. Review in Math Reviews: MR2001h81121.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.
http://journals.cms.math.ca/cgi-bin/vault/view/hall1006

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. Funct. Anal. 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. Review in Math Reviews: MR99e22015.pdf

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. Funct. Anal. 143 (1997), 98--116. jfa143.pdf

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