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

29. With K. Chailuek, Toeplitz operators on generalized Bergman spaces. To appear in Integral Equations and Operator Theory. IEOTfinal.pdf

28. With W. Kirwin, Adapted complex structures and the geodesic flow. Submitted for publication.

geodesic.pdf

27. Berezin-Toeplitz quantization on Lie groups, J. Functional Analysis 255 (2008), 2488–2506 (Special issue in honor of Paul Malliavin). Please e-mail me at bhall@nd.edu for a reprint.

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