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

Teaching

Math 5343 -- Functional Analysis

Math 4523 -- Advanced Calculus II

Celebration of the Mind materials


Publications and Preprints

  1. "$L^p$-estimates for the $\bar\partial$-equation on a class of infinite type domains", with Ly Kim Ha and Khanh Tran, submitted.
  2. "The Kerzman-Stein operator for piecewise continuously differentiable regions", with Michael Bolt, submitted. (arXiv:1208.2192)
  3. "Closed Range for $\bar\partial$ and $\bar\partial_b$ on Bounded Hypersurfaces in Stein Manifolds", with Phillip Harrington, submitted. (arXiv:1106.0629)
  4. "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)
  5. "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)
  6. "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).
  7. "Defining functions for unbounded $C^m$ domains", with Phillip Harrington, Rev. Mat. Iberoam. 29(4):1405-1420, 2013.
  8. "Fundamental solutions to $\Box_b$ on certain quadrics", with Albert Boggess, J. Geom. Analysis, 23(4):1729-1752, 2013. (arXiv:1110.5804)
  9. "Heat kernels, smoothness estimates and exponential decay", with Albert Boggess, J. Fourier Anal. Appl., 19:180-224, 2013.
  10. "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.
  11. "An Aronsson type approach to extremal quasiconformal mappings", with Luca Capogna, J. Differential Equations, 253:851-877, 2012.
  12. "Heat equations and the weighted $\bar\partial$-problem", Commun. Pure Appl. Anal., 11(3):885-909, 2012.
  13. "The $\Box_b$-heat equation on quadric manifolds", with Albert Boggess, J. Geom. Analysis, 21:256-275, 2011.
  14. "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)
  15. "Compactness of the complex Green operator on CR-manifolds of hypersurface type", Math. Ann., 348: 81-117, 2010. (arXiv:0810.2553)
  16. "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.
  17. "Compactness of the complex Green operator" , with Emil J. Straube. Math. Res. Lett., 15: 761-778, 2008.
  18. "Pointwise estimates for relative fundamental solutions of heat equations in $\mathbb{R}\times\mathbb{C}$", Math. Z., 256: 193-220, 2007.
  19. "Heat equations in $\mathbb{R}\times\mathbb{C}$" , J. Funct. Anal., 240: 1-35, 2006.
  20. "One-parameter families of operators in $\mathbb{C}$", J. Geom. Analysis, 16(2):353-374, 2006.
  21. "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.
  22. "Lightly mixing on dense algebras", with E. J. Muehlegger, C. E. Silva and W. Zhao. Real Analysis Exchange. 23:259-265, 1997/98.

Curriculum Vita

Curriculum Vita (.pdf format)

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