# Andy Raich

Associate Professor
Department of Mathematical Sciences
SCEN 327
1 University of Arkansas
Fayetteville, AR 72701
Fax: (479) 575-8630
Contact: araich@uark.edu

# Celebration of the Mind materials

## Curriculum Vita

Curriculum Vita (.pdf format)

## Publications and Preprints

1. "Local regularity properties for the Bergman projection on pseudoconvex domains of finite/infinite type", with Tran Vu Khanh, submitted.
2. "The Szeg\"o kernel on a class of noncompact CR manifolds of high codimension", with Michael Tinker, to appear Complex Var. Elliptic Equ..
3. "Taylor Series of Conformal Mappings onto Symmetric Quadrilaterals", with Loredana Lanzani and Jeanine Myers, to appear Complex Var. Elliptic Equ..
4. "Closed Range for $\bar\partial$ and $\bar\partial_b$ on Bounded Hypersurfaces in Stein Manifolds", with Phillip Harrington, to appear Ann. Inst. Fourier (Grenoble).
5. "The Kerzman-Stein operator for piecewise continuously differentiable regions", with Michael Bolt, to appear Complex Var. Elliptic Equ.. (arXiv:1208.2192)
6. "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.
7. "$L^p$-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).
8. "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)
9. "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.
10. "Defining functions for unbounded $C^m$ domains", with Phillip Harrington, Rev. Mat. Iberoam. 29(4):1405-1420, 2013.
11. "Fundamental solutions to $\Box_b$ on certain quadrics", with Albert Boggess, J. Geom. Analysis 23(4):1729-1752, 2013. (arXiv:1110.5804)
12. "Heat kernels, smoothness estimates and exponential decay", with Albert Boggess, J. Fourier Anal. Appl., 19:180-224, 2013.
13. "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.
14. "An Aronsson type approach to extremal quasiconformal mappings", with Luca Capogna, J. Differential Equations, 253:851-877, 2012.
15. "Heat equations and the weighted $\bar\partial$-problem", Commun. Pure Appl. Anal., 11(3):885-909, 2012.
16. "The $\Box_b$-heat equation on quadric manifolds", with Albert Boggess, J. Geom. Analysis, 21:256-275, 2011.
17. "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)
18. "Compactness of the Complex Green Operator on CR-Manifolds of Hypersurface Type", Math. Ann., 348: 81-117, 2010. (arXiv:0810.2553)
19. "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.
20. "Compactness of the Complex Green Operator", with Emil J. Straube. Math. Res. Lett., 15: 761-778, 2008.
21. "Pointwise Estimates for Relative Fundamental Solutions of Heat Equations in $\mathbb{R}\times\mathbb{C}$", Math. Z., 256: 193-220, 2007.
22. "Heat Equation in $\mathbb{R}\times\mathbb{C}$" , J. Funct. Anal., 240: 1-35, 2006.
23. "One-Parameter Families of Operators in $\mathbb{C}$", J. Geom. Analysis, 16(2):353-374, 2006.
24. "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.
25. "Lightly mixing on dense algebras", with E. J. Muehlegger, C. E. Silva and W. Zhao. Real Analysis Exchange. 23:259-265, 1997/98.