## Andy RaichAssociate ProfessorDepartment of Mathematical Sciences SCEN 327 1 University of Arkansas Fayetteville, AR 72701 Fax: (479) 575-8630 Contact: araich@uark.edu |

- "Zero sets of functions in the Nevanlinna class and the $\bar\partial_b$-equation on convex domains of general type in $\mathbb{C}^2$", with Khan Tran, submitted.
- "Global $L^q$ Gevrey Functions, Paley-Weiner Theorems, and the FBI Transform", with Gustavo Hoepfner, submitted.
- "Estimates of the Newtonian potential on bounded domains", with Tran Vu Khanh, submitted.
- "A remark on boundary estimates on unbounded $Z(q)$ domains in $\mathbb C^n$", with Phillip Harrington, submitted.
- "Global $L^q$-Gevrey functions and their applications", with Ziad Adwan and Gustavo Hoepfner, submitted.
- "Local regularity of the Bergman projection on a class of pseudoconvex domains of finite type", with Tran Vu Khanh, submitted.
- "Closed range of $\bar\partial$ on unbounded domains in $\mathbb{C}^n$", with Phillip Harrington, submitted.
- "Schr\"odinger Operators With $A_\infty$ Potentials", with Michael Tinker, to appear,
*Potential Analysis* - "Green's function asymptotics near the internal edges of spectra of periodic elliptic operators. Spectral gap interior", with Minh Kha and Peter Kuchment,
to appear,
*Journal of Spectral Theory*. -
"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. (ariXiv:1408.4182) - "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) - "Taylor Series of Conformal Mappings onto Symmetric Quadrilaterals", with Loredana Lanzani and Jeanine Myers,
*Complex Var. Elliptic Equ.*,**60**(8): 1133-1141, 2015. - "The Kerzman-Stein operator for piecewise continuously differentiable regions", with Michael Bolt,
*Complex Var. Elliptic Equ.*,**60**(4): 478-492, 2015. (arXiv:1208.2192) -
"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. - "$L^p$-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). - "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) - "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. - "Defining functions for unbounded $C^m$ domains", with Phillip Harrington,
*Rev. Mat. Iberoam.***29**(4):1405-1420, 2013. - "Fundamental solutions to $\Box_b$ on certain quadrics", with Albert Boggess,
*J. Geom. Analysis***23**(4):1729-1752, 2013. (arXiv:1110.5804) -
"Heat kernels, smoothness estimates and exponential decay", with
Albert Boggess,
*J. Fourier Anal. Appl.*,**19**:180-224, 2013. - "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. -
"An Aronsson type approach to extremal quasiconformal mappings", with Luca Capogna,
*J. Differential Equations*,**253**:851-877, 2012. - "Heat equations and the weighted $\bar\partial$-problem",
*Commun. Pure Appl. Anal.*,**11**(3):885-909, 2012. - "The $\Box_b$-heat equation on quadric manifolds", with Albert Boggess,
*J. Geom. Analysis*,**21**:256-275, 2011. - "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) - "Compactness of the Complex Green Operator on CR-Manifolds of Hypersurface Type",
*Math. Ann.,***348**: 81-117, 2010. (arXiv:0810.2553) -
"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. - "Compactness of the Complex Green Operator", with Emil J. Straube.
*Math. Res. Lett.*,**15**: 761-778, 2008. -
"Pointwise Estimates for Relative Fundamental Solutions of Heat Equations
in $\mathbb{R}\times\mathbb{C}$",
*Math. Z.*,**256**: 193-220, 2007. - "Heat Equation in
$\mathbb{R}\times\mathbb{C}$"
,
*J. Funct. Anal.*,**240**: 1-35, 2006. - "One-Parameter Families of
Operators in $\mathbb{C}$",
*J. Geom. Analysis*,**16**(2):353-374, 2006. - "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. - "Lightly mixing on dense algebras", with E. J. Muehlegger,
C. E. Silva
and W. Zhao.
*Real Analysis Exchange*.**23**:259-265, 1997/98.