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Last updated Feb 2011
- Born: January 1, 1950
- Married to Jan K (nee Nelson), 2 children,
Lindsay N. (Matthews) Ball and Nicholas D. Luecking.
- 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
- 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
- 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
- Thomas Limperis, Ph.D., " Embedding Theorems for the Bloch
- Phuc K. Nguyen, Ph.D., "Interpolation and Sampling Sequences for Mixed-norm
- Newton H. Foster, Ph.D,. "A General Sampling Scheme for Bergman
Grants And Awards
- University of Illinois University Fellowship, 1974-1976
- National Science Foundation Graduate Fellowship, 1971-1974
- 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
- College of Arts and Sciences full-time research appointment,
- Mittag-Leffler Institute, May, 1991
- College of Arts and Sciences full-time research appointment,
Current Research Activity
Preprints and work in progress
I have some completed preprints
offered for download.
- Badly approximable functions and uniform algebras,
J. Approximation Theory, 22 (1978), 161-176.
- The compact Hankel operators form an M-ideal in the space
of Hankel operators, Proc. Amer. Math. Soc., 79 (1980),
- Inequalities in Bergman spaces, Ill, J. Math., 25 (1981),
- Division in Douglas algebras, Michigan Math. J., 29
- A technique for characterizing Carleson measures on
Bergman spaces, Proc. Amer. Math. Soc., 87 (1983),
- Quotients of L^\infty by Douglas algebras and best
approximation, Transactions of Amer. Math. Soc., 276
(1983), 699-706 (with R. Younis).
- Equivalent norms for Lp spaces of harmonic functions,
Monatsefte fur Math., 96 (1983), 133-141.
- Closed-range restriction operators on weighted Bergman
spaces, Pacific J. Math., 110 (1984), 145-160.
- Complex Analysis: A Functional Analysis Approach,
Universitext, 176 pp. Spring-Verlag, New York, 1984 (with
Lee A. Rubel).
- Forward and reverse Carleson inequalities for functions in
Bergman spaces and their derivatives, Amer. J. Math.
107 (1985), 85-111.
- Representation and duality in weighted spaces of analytic
functions, Indiana Univ. Math. J. 34 (1985), 319-336.
- Boundary behavior of Green potentials, Proc. Amer. Math.
Soc., 96 (186), 481-488.
- On an extremal problem in the theory of rational
approximation, J. Approx. Theory, 50 (1987), 127-132
(with D. Khavinson).
- Multipliers of Bergman spaces into Lebesgue spaces, Proc.
Edinburgh Math. Soc., 29 (1986), 125-131.
- Trace ideal criteria for Toeplitz operators, J.
Functional Analysis, 73 (1987), 345-368.
- Dominating measures for spaces of analytic functions,
Ill. J. Math., 31 (1988), 23-39.
- A new proof of an inequality of Littlewood and Paley,
Proc. Amer. Math. Soc. 103 (1988), 887-893.
- Embedding derivatives of Hardy Spaces into Lebesque
spaces, Proc. London Math. Soc., 63 (1991), 595-619.
- Composition Operators belonging to the Schatten ideals,
Amer. J. Math, 114 (1992), 1127-1145 (with Kehe Zhu).
- Embedding theorems for spaces of analytic functions via
Khinchine's inequality, Michigan Math. J., 40 (1993),
- Characterizations of certain class of Hankel operators on
the Bergman spaces of the unit disk, J. Functional Anal.,
110 (1992), 247-271.
- BMO on strongly pseudoconvex domains: Hankel operators,
duality and d-bar estimates, Trans. Amer. Math. Soc., 346
(1994), 661-691 (with Huiping Li).
- Schatten Class of Hankel and Toeplitz operators on the
Bergman space of strongly pseuoconvex domains,
Contemporary Math., 185 (1995), 237--257 (with Huiping Li).
- Zero sequences for Bergman spaces, Complex Variables, 30
- The Dual of Bergman metric VMO, Rocky Mountain J. Math., 29,
- Bounded composition operators with closed range on the Dirichlet
space, Proc. Amer. Math. Soc., 128 (2000),1109--1116.
- Sampling measures for Bergman spaces on the unit disk,
Math. Ann., 316 (2000), 659--679.
- On the value of pi for norms in R^2, The College Math. J., 35,
(2003), 84--92 (with J. Duncan and C. McGregor).
- Interpolating Sequences for the Bergman spaces and the
d-bar equation in weighted Lp, submitted.
- Finite rank Toeplitz operators on the Bergman space, Proc.
Amer. Math. Soc., 136 (2007) 1717--1723.
- Library Committee (1981-89, 1990-2009; Chair,
- Spring Lecture Series Committee (1984-85, 1986-89,
- Steering Committee (1993--96, 2001--2004)
- Graduate Committee (2005--2008) and (2016--present)
- Graduate Chair, (2006--2007) and (2014--2016)
- Faculty Development Committee (Spring 1991)
- CSCI Promotion and Tenure Committee (1994--97)
- Graduate Council (1998--99)
Invited Presentations (Since 1989 only)
- Trinity College, Dublin, Ireland (1989)
- Wayne State University, Detroit (1995)
- Southeastern Analysis Meeting at Athens, GA (1989)
- Irish Mathematical Society Meeting at Maynooth, Ireland
- 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,
- 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,
- AMS Special Session on Complex Analysis at Memphis, TN
- 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
- AMS Special Session on Holomorphic Spaces at San Francisco, CA
- 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
- AMS Special Session on Operator Theory on Function Spaces at
Nashville, TN (2004)
- International Workshop in Function Theory at Seoul, S. Korea
- 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)
luecking at uark dot edu