Personal

• Born: January 1, 1950
• Married to Jan K (nee Nelson), 2 children, Lindsay N. (Matthews) Ball and Nicholas D. Luecking.

Education

• Ph.D. University of Illinois, Urbana, IL, 1976
• M.S. University of Illinois, Urbana, IL, 1972
• B.A. Southern Illinois University at Edwardsville, IL 1971
• Ph.D. Thesis: A function algebra approach to badly approximable functions Thesis Advisor: Lee A. Rubel

Professional Experience

Positions Held

• Professor, University of Arkansas, 1990-Present
• Visiting Lecturer, Trinity College, Dublin, Ireland, 1989/90
• Associate Professor, University of Arkansas, 1984-1990
• Visiting Assistant Professor, University of Tennessee, Winter and Spring, 1984
• Assistant Professor, University of Arkansas, 1981-1984
• Assistant Professor, Michigan State University, 1978-1981
• C.L.E. Moore Research Instructorship MIT, 1976-1978

Teaching

• Undergraduate: College algebra, finite mathematics, calculus, honors calculus, differential equations, linear algebra, discrete math, combinatorics, applied mathematics, advanced calculus, real and complex analysis
• Graduate: real and complex analysis, functional analysis, topics in analysis, topology

Theses directed

1. Thomas Limperis, Ph.D., " Embedding Theorems for the Bloch Space", 1998
2. Phuc K. Nguyen, Ph.D., "Interpolation and Sampling Sequences for Mixed-norm Spaces", 2011
3. Newton H. Foster, Ph.D,. "A General Sampling Scheme for Bergman Spaces", 2014

Grants And Awards

Fellowships

• University of Illinois University Fellowship, 1974-1976
• National Science Foundation Graduate Fellowship, 1971-1974

Grants

• NSF Summer Research Grants (co-investigator), 1977-1978.
• University of Arkansas Research Incentive Grant, 1982
• NSF Research Grant #MCS-8201603, 1982-1984, "Closed range embedding of Bergman spaces"
• NSF Research Grant #DMS-8201603, 1984-1986, "Operators on Bergman Spaces."

Other awards

• College of Arts and Sciences full-time research appointment, Spring 1985.
• Mittag-Leffler Institute, May, 1991
• College of Arts and Sciences full-time research appointment, Fall 1991.

Current Research Activity

Preprints and work in progress

I have some completed preprints offered for download.

Publications (refereed)

1. Badly approximable functions and uniform algebras, J. Approximation Theory, 22 (1978), 161-176.
2. The compact Hankel operators form an M-ideal in the space of Hankel operators, Proc. Amer. Math. Soc., 79 (1980), 22-224.
3. Inequalities in Bergman spaces, Ill, J. Math., 25 (1981), 1-11.
4. Division in Douglas algebras, Michigan Math. J., 29 (1982), 307-314.
5. A technique for characterizing Carleson measures on Bergman spaces, Proc. Amer. Math. Soc., 87 (1983), 656-660.
6. Quotients of L^\infty by Douglas algebras and best approximation, Transactions of Amer. Math. Soc., 276 (1983), 699-706 (with R. Younis).
7. Equivalent norms for Lp spaces of harmonic functions, Monatsefte fur Math., 96 (1983), 133-141.
8. Closed-range restriction operators on weighted Bergman spaces, Pacific J. Math., 110 (1984), 145-160.
9. Complex Analysis: A Functional Analysis Approach, Universitext, 176 pp. Spring-Verlag, New York, 1984 (with Lee A. Rubel).
10. Forward and reverse Carleson inequalities for functions in Bergman spaces and their derivatives, Amer. J. Math. 107 (1985), 85-111.
11. Representation and duality in weighted spaces of analytic functions, Indiana Univ. Math. J. 34 (1985), 319-336.
12. Boundary behavior of Green potentials, Proc. Amer. Math. Soc., 96 (186), 481-488.
13. On an extremal problem in the theory of rational approximation, J. Approx. Theory, 50 (1987), 127-132 (with D. Khavinson).
14. Multipliers of Bergman spaces into Lebesgue spaces, Proc. Edinburgh Math. Soc., 29 (1986), 125-131.
15. Trace ideal criteria for Toeplitz operators, J. Functional Analysis, 73 (1987), 345-368.
16. Dominating measures for spaces of analytic functions, Ill. J. Math., 31 (1988), 23-39.
17. A new proof of an inequality of Littlewood and Paley, Proc. Amer. Math. Soc. 103 (1988), 887-893.
18. Embedding derivatives of Hardy Spaces into Lebesque spaces, Proc. London Math. Soc., 63 (1991), 595-619.
19. Composition Operators belonging to the Schatten ideals, Amer. J. Math, 114 (1992), 1127-1145 (with Kehe Zhu).
20. Embedding theorems for spaces of analytic functions via Khinchine's inequality, Michigan Math. J., 40 (1993), 333-358.
21. Characterizations of certain class of Hankel operators on the Bergman spaces of the unit disk, J. Functional Anal., 110 (1992), 247-271.
22. BMO on strongly pseudoconvex domains: Hankel operators, duality and d-bar estimates, Trans. Amer. Math. Soc., 346 (1994), 661-691 (with Huiping Li).
23. Schatten Class of Hankel and Toeplitz operators on the Bergman space of strongly pseuoconvex domains, Contemporary Math., 185 (1995), 237--257 (with Huiping Li).
24. Zero sequences for Bergman spaces, Complex Variables, 30 (1996), 345--362.
25. The Dual of Bergman metric VMO, Rocky Mountain J. Math., 29, (1999), 1413--1428.
26. Bounded composition operators with closed range on the Dirichlet space, Proc. Amer. Math. Soc., 128 (2000),1109--1116.
27. Sampling measures for Bergman spaces on the unit disk, Math. Ann., 316 (2000), 659--679.
28. On the value of pi for norms in R^2, The College Math. J., 35, (2003), 84--92 (with J. Duncan and C. McGregor).
29. Interpolating Sequences for the Bergman spaces and the d-bar equation in weighted Lp, submitted.
30. Finite rank Toeplitz operators on the Bergman space, Proc. Amer. Math. Soc., 136 (2007) 1717--1723.

Committees

Departmental

• Library Committee (1981-89, 1990-2009; Chair, 1991-2009)
• Spring Lecture Series Committee (1984-85, 1986-89, 1993--2014)
• Steering Committee (1993--96, 2001--2004)
• Graduate Committee (2005--2008) and (2016--present)
• Graduate Chair, (2006--2007) and (2014--2016)

University

• Faculty Development Committee (Spring 1991)
• CSCI Promotion and Tenure Committee (1994--97)
• Graduate Council (1998--99)

Invited Presentations (Since 1989 only)

Colloquia

• Trinity College, Dublin, Ireland (1989)
• Wayne State University, Detroit (1995)

Others

• Southeastern Analysis Meeting at Athens, GA (1989)
• Irish Mathematical Society Meeting at Maynooth, Ireland (1989)
• University College, Cork, Ireland, Analysis Seminar (1990)
• University of Edinburgh, Scotland, Analysis Seminar (1990)
• Yorkshire Functional Analysis Colloquium, University of Leeds, U.K. (1990)
• Trinity College Analysis Seminar, Dublin Ireland (1990)
• Mittag-Leffler Institute Seminar 1991
• AMS Special Session on Bergman Spaces at Baltimore (1992)
• Function Theory and Algebraic Differential Equations, Urbana, Ill. (1993)
• AMS Special Session on Composition operators on spaces of Analytic functions at College Station, TX (1993)
• AMS Special Session on Operator Theory at Manhattan, Kansas (1994)
• Joint Summer Research Conference: Bergman spaces and the operators that act on them, South Hadley, Mass.
• AMS Special Session on Operators on Banach spaces of analytic functions at Richmond, Va. (1994)
• AMS Special Session on Holomorphic spaces at San Francisco, CA (1995)
• AMS Special Session on Complex Analysis at Memphis, TN (1997)
• AMS Special Session on Operator Theory and Function Spaces at Milwaukee, WI (1997)
• AMS Special Session on Operator Theory and Holomorphic Spaces at Winston-Salem, NC (1998)
• AMS Special Session on Banach Spaces of Holomorphic Functions and Operators on these Spaces at San Antonio, TX (1999)
• Southeasterm Analysis Meeting (SEAM), Charlottesville, VA (2000)
• AMS Special Session on Holomorphic Spaces at San Francisco, CA (2000)
• AMS Special Session in Operator Theory on Function Spaces, New Orleans, LA (2001)
• Southeastern Analysis Meeting (SEAM), Chapel Hill, NC (2002)
• Southeastern Analysis Meeting (SEAM), Knoxville, TN (2003)
• AMS Special Session on Modern Function Theory at Phoenix, AZ (2004)
• AMS Special Session on Operator Theory on Function Spaces at Nashville, TN (2004)
• International Workshop in Function Theory at Seoul, S. Korea (IWFT2005)
• Southeastern Analysis Meeting (SEAM), Richmond, VA (2007)
• University of Toledo Shoemaker Lectures (featured speaker), Toledo, OH (2007)
• Southeastern Analysis Meeting (SEAM), Tampa, FL (2009)
• Southeastern Analysis Meeting (SEAM), Atlanta, GA (2010)