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# 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 co-organized 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 Brooks** - Several Complex Variables & Harmonic Analysis

**Prof. Greg St. George** - Functional Analysis

**Prof. Karel Stroethoff** - Complex & Functional Analysis, Operator Theory

### 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, Shift-Invariant Uniform Algebras on Groups, Monografie Matematyczne, v. 68, New Series, Birkhauser Verlag, Basel-Boston-Berlin, 2006, 284 pp. (with S. Grigoryan).
- Thomas Tonev, Big-Planes, Boundaries and Function Algebras, Elsevier - North-Holland, 1992, 294 pp.
- Thomas Tonev, Continued Fractions, Narodna Prosveta, Sofia, 1989, 122 pp. (with E. Lyubenova-Toneva).

### 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 non-pseudoconvex 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 Non-Pseudoconvex 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), 75-128.
- 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:1304-0237[math.CV],[math.AC].
- Thomas Tonev, Norm-linear and norm-additive operators between uniform algebras, Journal of Math. Anal. and Appl. (2009) (with R. Yates - UM PhD student)
- Thomas Tonev, Weakly Peripherally-Multiplicative 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. Thomas Tonev** - Complex & Functional Analysis, Commutative Banach Algebras

**Prof. George Votruba** - Functional Analysis, Approximation Theory, Linear Algebra

**Prof. Keith Yale** - Harmonic & Functional Analysis