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

Math 3513 -- Elementary Analysis

- "The Szeg\"o kernel on a class of noncompact CR manifolds of high codimension", with Michael Tinker, submitted.
- "Local regularity properties for the Bergman projection on pseudoconvex domains of finite/infinite type", with Tran Vu Khanh, submitted.
- "Taylor Series of Conformal Mappings onto Symmetric Quadrilaterals", with Loredana Lanzani and Jeanine Myers, submitted.
- "$L^p$-Estimates for the $\bar\partial$-equation on a class of infinite type domains", with Ly Kim Ha and Khanh Tran, submitted.
- "Closed Range for $\bar\partial$ and $\bar\partial_b$ on Bounded Hypersurfaces in Stein Manifolds", with Phillip Harrington, submitted.
- "The Kerzman-Stein operator for piecewise continuously differentiable regions", with Michael Bolt,
*Complex Var. Elliptic Equ.*. (arXiv:1208.2192) - "Regularity equivalence of the Szeg\"o projection and the complex Green operator",
with Phillip Harrington and Marco Peloso, to appear
*Proc. Amer. Math. Soc.*. (arXiv:1305.0188) - "Div-curl type inequalities for higher order operators", with Loredana Lanzani, to appear
*Advances in Analysis: The Legacy of Elias M. Stein*(Princeton Mathematical Series). - "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) - "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.

- Analysis Seminar , University of Arkansas
- University of Arkansas Department of Mathematical Sciences
- American Mathematical Society
- MathSciNet
- arXiv: Mathematics
- The Mathematics Genealogy Project
- JSTOR Math Journals
- Emil Straube
- Alex Nagel