Analysis

The Department of Mathematical Sciences has a very active group of analysts whose research interests lie in the areas of complex analysis in one and several variables, functional analysis, commutative Banach algebras, harmonic analysis, and operator theory. We have a weekly analysis seminar for faculty and graduate students. We discuss several different topics in the seminar throughout the year, with each participant typically giving three to five lectures.
Distinguished analysts also visit the department each year to give lectures and to collaborate with members of the faculty. Recent visitors include M. Hayashi, O. Hatori, T. Miura, L. Molnar, F. Jafari, N. Rao, J. Cima, P. Harrington, M. Pramanik, and D. Grundmeier. .
Members of the group have coorganized special sessions in Analysis at meetings of the American Mathematical Society in San Francisco, Lawrence KS, Morelia, Mexico, etc. They also give invited talks at regional, national, and international conferences and at universities across the country.

Analysis Faculty

Prof. Jennifer Halfpap Kacmarcik  Several Complex Variables & Harmonic Analysis
Prof. Greg St. George  Functional Analysis
Prof. Karel Stroethoff  Complex & Functional Analysis, Operator Theory
Prof. Thomas Tonev  Complex & Functional Analysis, Commutative Banach Algebras
Recent Grants:
NSF DMS 1200815 "CR Manifolds and Singular Integrals", PI: Halfpap
2011 Simons Foundation Collaboration Grant. PI: Tonev
NSF DMS 0654195 "Singular Integral Operators in Several Complex Variables", PI: Halfpap
Books:
Thomas Tonev, ShiftInvariant Uniform Algebras on Groups, Monografie Matematyczne, v. 68, New Series, Birkhauser Verlag, BaselBostonBerlin, 2006, 284 pp. (with S. Grigoryan).
Thomas Tonev, BigPlanes, Boundaries and Function Algebras, Elsevier  NorthHolland, 1992, 294 pp.
Thomas Tonev, Continued Fractions, Narodna Prosveta, Sofia, 1989, 122 pp. (with E. LyubenovaToneva).
Selected publications:
J. Halfpap and J. Lebl, Signature pairs for positive polynomials, Bulletin of the Society of Mathematics, Academia Sinica, New Series, 8, (2013) . See also arXiv:1211.0997v2 [math.AG],[math.CV].
M. Gilliam and J. Halfpap, The Szego kernels for nonpseudoconvex tube domains in C2, Complex Variables and Elliptic Equations, (to appear 2013). See also arXiv:1107.1694v1[math.CV].
M. Gilliam and J. Halfpap, The Szego Kernel for Certain NonPseudoconvex Domains in C2, Illinois J. Math., 55, (2011), no. 3, 871  894 (2013). See also arXiv:1107.1687v1 [math.CV].
J. Halfpap, A. Nagel, and S. Wainger, The Bergman and Szego Kernels near Points of Infinite Type, Pacific Journal of Mathematics, 246(1), (2010), 75128.
D. Grundmeier and J. Halfpap, An Application of Macaulay's Estimate to sums of squares problems, Proceedings of the AMS, to appear. See also arXiv:13040237[math.CV],[math.AC].
Thomas Tonev, Normlinear and normadditive operators between uniform algebras, Journal of Math. Anal. and Appl. (2009) (with R. Yates  UM PhD student)
Thomas Tonev, Weakly PeripherallyMultiplicative Mappings Between Uniform Algebras, Contemporary Math., Amer. Math. Soc. (2007) (with S. Lambert and A. Luttman  UM PhD Students).
Thomas Tonev, Uniform algebra isomorphisms and peripheral spectra, Contemporary Math., Amer. Math. Soc. (2007) (with N. Rao and E. Toneva).

Emeritus Faculty

Prof. George Votruba  Functional Analysis, Approximation Theory, Linear Algebra
Prof. Keith Yale  Harmonic & Functional Analysis

