Andy Raich

Curriculum Vita

Publications and Preprints

1. "Analysis on Quadrics", with Al Boggess, submitted. *
2. "Weighted Hardy Space and Ultradistributions", with Gustavo Hoepfner and Patricia Rampazo, submitted.
3. "The Fundamental Solution to $\Box_b$ on Quadric Manifolds with Nonzero Eigenvalues", with Al Boggess, submitted.
4. "Global Gevrey Vectors", with G. Hoepfner and P. Rampazo, submitted.
5. "Distributions with Decay and Restriction Problems", with Gustavo Hoepfner, submitted.
6. "Boundary invariants and the closed range property for $\bar\partial$", with Phillip Harrington, submitted.
7. "The Fundamental Solution to $\Box_b$ on Quadric Manifolds -- Part 3. Asymptotics for a Codimension 2 case in $\mathbb{C}^4$", with Al Boggess, to appear, J. Geom. Anal..
8. "The Fundamental Solution to $\Box_b$ on Quadric Manifolds -- Part 1. General Formulas", with Al Boggess, to appear, Proc. Amer. Math Soc.
9. "Strong Closed Range Estimates: Necessary Conditions and Applications", with Phillip Harrington, to appear, Indiana Univ. Math. J.
10. "Compactness of the complex Green operator on non-pseudoconvex CR manifolds", with Joel Coacalle, Commun. Pure Appl. Anal., 20(6):2139--2154, 2021.
11. "Closed range estimates for $\bar\partial_b$ on CR manifolds of hypersurface type", with Joel Coacalle, J. Geom. Anal., 31(1): 366--394, 2021.
12. "$L^p$-Estimates for the $\bar\partial_b$-equation on a class of infinite type domains", with Khanh Tran, Math. Nachr., 294(1):82--97, 2021.
13. "The complex Green operator with Sobolev estimates up to a finite order," with Bingyuan Liu, Internat. J. Math., 31(14), 2050122, 19pp, 2020.
14. "The Kohn-Laplace equation on abstract CR manifolds: Global regularity", with Khanh Tran, Trans. Amer. Math. Soc., 373(11): 7575--7606, 2020.
15. "The Fundamental Solution to $\Box_b$ on Quadric Manifolds -- Part 2. $L^p$ Regularity and Invariant Normal Forms", with Al Boggess, Complex Anal. Synerg., 6(2): Paper No. 13, 19pp, 2020.
16. "Closed range of $\bar\partial$ on unbounded domains in $\mathbb{C}^n$", with Phillip Harrington, J. Anal. Math., 138(1):185--208, 2019.
17. "Global $L^q$ Gevrey Functions, Paley-Weiner Theorems, and the FBI Transform", with Gustavo Hoepfner, Indiana Univ. Math. J, 68(3): 967--1002, 2019.
18. "Microglobal Regularity and the Global Wavefront Set", with Gustavo Hoepfner, Math. Z. 291(3-4): 971--988, 2019.
19. "The Bergman Kernel on Forms: General Theory, Proc. Amer. Math Soc., 146(11): 4683--4692, 2018.
20. "Closed range of $\bar\partial$ in $L^2$-Sobolev spaces on unbounded domains in $\mathbb C^n$", with Phillip Harrington, J. Math. Anal. Appl459(2): 1040--1061, 2018.
21. "Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior", with Minh Kha and Peter Kuchment, Journal of Spectral Theory, 7(4): 1171--1233, 2017
22. "WHAT IS a CR Manifold?", with Phillip Harrington, Notices Amer. Math. Soc., 64(7): 722-724, 2017.
23. "Global $L^q$-Gevrey functions and their applications", with Ziad Adwan and Gustavo Hoepfner, J. Geom. Anal., 27(3): 1874-1913, 2017.
24. "A remark on boundary estimates on unbounded $Z(q)$ domains in $\mathbb C^n$", with Phillip Harrington, Complex Var. Elliptic Equ., 62(9): 1192-1203, 2017. (arXiv:1512.02523)
25. "Schr\"odinger Operators With $A_\infty$ Potentials", with Michael Tinker, Potential Analysis, 45(2): 387-402, 2016.
26. "Closed Range for $\bar\partial$ and $\bar\partial_b$ on Bounded Hypersurfaces in Stein Manifolds", with Phillip Harrington, Ann. Inst. Fourier (Grenoble), 65(4): 1711-1754, 2015. (arXiv:1408.4182)
27. "The Szeg\"o kernel on a class of noncompact CR manifolds of high codimension", with Michael Tinker, Complex Var. Elliptic Equ., 60(10): 1366-1373, 2015. (ariXiv:1408.4182)
28. "Taylor Series of Conformal Mappings onto Symmetric Quadrilaterals", with Loredana Lanzani and Jeanine Myers, Complex Var. Elliptic Equ., 60(8): 1133-1141, 2015.
29. "The Kerzman-Stein operator for piecewise continuously differentiable regions", with Michael Bolt, Complex Var. Elliptic Equ., 60(4): 478-492, 2015. (arXiv:1208.2192)
30. "Regularity equivalence of the Szeg\"o projection and the complex Green operator", with Phillip Harrington and Marco Peloso, Proc. Amer. Math. Soc., 143(1): 353-367, 2015.
31. "$L^p$-Estimates for the $\bar\partial$-equation on a class of infinite type domains", with Ly Kim Ha and Khanh Tran, Internat. J. Math., 25(11): 2014. 1450106 (15 pages).
32. "Sobolev spaces and elliptic theory on unbounded domains in $\mathbb R^n$", with Phillip Harrington, Adv. Differential Equations, 19(7/8): 635-692, 2014. (arXiv:1209.4044)
33. "Div-curl type inequalities for higher order operators", with Loredana Lanzani, Advances in Analysis: The Legacy of Elias M. Stein (Princeton Mathematical Series). Princeton U. Press, (2013). ISBN: 9780691159416.
34. "Defining functions for unbounded $C^m$ domains", with Phillip Harrington, Rev. Mat. Iberoam. 29(4):1405-1420, 2013.
35. "Fundamental solutions to $\Box_b$ on certain quadrics", with Albert Boggess, J. Geom. Analysis 23(4):1729-1752, 2013. (arXiv:1110.5804)
36. "Heat kernels, smoothness estimates and exponential decay", with Albert Boggess, J. Fourier Anal. Appl., 19:180-224, 2013.
37. "Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral edge case.", with Peter Kuchment, Math. Nachr, 285:1880-1894, 2012.
38. "An Aronsson type approach to extremal quasiconformal mappings", with Luca Capogna, J. Differential Equations, 253:851-877, 2012.
39. "Heat equations and the weighted $\bar\partial$-problem", Commun. Pure Appl. Anal., 11(3):885-909, 2012.
40. "The $\Box_b$-heat equation on quadric manifolds", with Albert Boggess, J. Geom. Analysis, 21:256-275, 2011.
41. "Regularity results for $\bar\partial_b$ on CR-manifolds of hypersurface type", with Phillip Harrington, Comm. Partial Differential Equations. 36:134-161, 2011.(arXiv:0912.2823)
42. "Compactness of the Complex Green Operator on CR-Manifolds of Hypersurface Type", Math. Ann., 348: 81-117, 2010. (arXiv:0810.2553)
43. "A Simplified Calculation for the Fundamental Solution to the Heat Equation on the Heisenberg Group", with Albert Boggess, Proc. Amer. Math. Soc., 137:937-944, 2009.
44. "Compactness of the Complex Green Operator", with Emil J. Straube, Math. Res. Lett. 15: 761--778, 2008.
45. "Pointwise Estimates for Relative Fundamental Solutions of Heat Equations in $\mathbb{R}\times\mathbb{C}$", Math. Z., 256: 193-220, 2007.
46. "Heat Equation in $\mathbb{R}\times\mathbb{C}$", J. Funct. Anal., 240: 1-35, 2006.
47. "One-Parameter Families of Operators in $\mathbb{C}$", J. Geom. Analysis, 16(2):353-374, 2006.
48. "Infinite ergodic index $\mathbb{Z}^d-actions in infinite measure$", with E. J. Muehlegger, C. E. Silva, M. P. Touloumtzis, B. Narasimhan and W. Zhao. Colloq. Math, 82:167-190, 1999.
49. "Lightly mixing on dense algebras", with E. J. Muehlegger, C. E. Silva and W. Zhao. Real Analysis Exchange. 23:259-265, 1997/98.

Miscellaneous

• My Academic Genealogy