Research

Prof. Cowen works in areas related to linear operators on Hilbert spaces of analytic functions such as the Hardy and Bergman spaces. Much of this research deals with the classical Toeplitz, composition, and weighted composition operators and the theory of analytic functions connected to these operators. The goal of this research is to connect the operator theoretic structure of operators with the geometric and analytic structure of the functions defining the operator. Cowen's PhD students have worked in operator theory and related linear algebra and theory of analytic functions.

Publications & Professional Activity

1. Cowen, C. C., An analytic Toeplitz operator that commutes with a compact operator, J. Functional Anal., 36(1980) 169-184.

2. Cowen, C. C., Iteration and the Solution of Functional Equations for Functions Analytic in the Unit Disk,  Trans. Amer. Math. Soc.,  265(1981) 69-95.

3. Cowen, C. C., Composition operators on H2, J. Operator Theory, 9(1983) 77-106.

4. Cowen, C. C., and MacCluer, B. D., Composition Operators on Spaces of Analytic Functions, CRC Press, Boca Raton, 1995. (xii+388 pages)

5. Cowen, C. C., and MacCluer, B. D., Linear fractional maps of the ball and their composition operators, Acta Sci. Math. (Szeged), 66(2000) 351-376.

6. Cowen, C. C., and MacCluer, B. D., Schroeder's equation in several variables. Taiwanese J. of Mathematics, 7(2003) 129-154.

7. Cowen, C. C., and Gallardo-Gutierrez, E. A., A new class of operators and a description of adjoints of composition operators, J. Functional Anal. 238(2006) 447-462.

8. Cowen, C. C., and Gallardo-Gutierrez, E. A., Unitary equivalence of one-parameter groups of Toeplitz and composition operators, J. Functional Anal. 261(2011) 2641-2655.

9. Cowen, C. C., Gunatillake, G., and Ko, E.I., Hermitian weighted composition operators and Bergman extremal functions. Complex Analysis Operator Theory 7(2013) 69-99.

10. Cowen, C. C., and Gallardo-Gutierrez, E. A., Rota's Universal Operators and Invariant Subspaces in Hilbert Spaces, J. Functional Anal. 271(2016) 1130-1149.

Affiliations

• American Mathematical Society
• Mathematical Association of America
• Society for Industrial and Applied Mathematics
• Real Sociedad Matématica Española
• International Linear Algebra Society
• Association for Women in Mathematics
• Society for Advancement of Chicanos and Native Americans in Science
• American Association for the Advancement of Science
• Mentor, National Alliance for Doctoral Studies in the Mathematical Sciences; 2016-
• Member, Editorial Advisory Board for "Journal of Humanistic Mathematics" 2009-
• Member, NAEP (National Assessment of Educational Progress) Math Standing Committee 2008-
• Consultant for Project NExT, 1995-
• AAAS (Amer. Assoc. Adv. Science), Math Section, Nominating Comm. 2010-13
• AMS Representative, Program Committee for "First International Congress on Mathematics and Statistics" held March, 2010 at Univ. of Sharjah, UAE
• Member, Editorial Board for book series "Issues in Mathematics Education"
• (CBMS/AMS) 2008-2010
• Member, Steering Committee, Forum on the National Math Panel Report, 2008-09
• Member, Advisory Board, Institute for Mathematics and Education, U. of Arizona, 2007-2010
• President, Mathematical Association of America, 2005-2007
• Past President, SIGMAA on Mathematical and Computational Biology 2006-2008
• First Vice President, Mathematical Association of America, 2002-2004
• MAA Coordinating Council on Education, 1996-2002, Chair, 2000-2002
• Project Director, AMS Task Force on Excellence in Mathematics Scholarship, 1995-97
• Indiana Section Governor, Board of Governors, Mathematical Association of America, 1996-1999
• SIAM Committee on Education, 1995-2001
• AMS Committee on Education, 1993-97, 2000-2003
• Member-at-Large, Council, American Mathematical Society, 1992-95
• Co-Chair and Purdue Coordinator for Wabash Modern Analysis Seminar 1984-2001
• Chair, Indiana Section of the Mathematical Association of America, 1989-90 & 82-83

Awards

• Bernie Morrel Teaching Award, IUPUI Mathematical Sciences Dept. 2010
• Mathematical Association of America Certificate for Meritorious Service 2009
• Indiana Section MAA Distinguished Service Award 2003
• Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching 1997
• Indiana Section MAA Award for Distinguished College or University Teaching 1995
• School of Science Outstanding Undergraduate Teaching Award 1985-86
• Marshall Scholarship
• Phi Beta Kappa
• Simons Foundation Grant, 2015-2020
• Plan Nacional I+D Grants, Gobierno de España y Gobierno de Aragon, 2009, 2012
• National Science Foundation Grants, 1976-1998, 2003-2004