**CURRICULUM VITA**

ALFRED S. CAVARETTA, JR.

October 4, 2007

Date of
birth:
June 16, 1944

Date of
hire:
1973

Current
rank:
Professor, Department of Mathematical Sciences, Kent
State University

Graduate Faculty Status: Full Member since
1975

EDUCATION

1966 B.A. Mathematics,

1968 M.A. Mathematics,

1970 Ph.D. University of Wisconsin, Madison

PROFESSIONAL EXPERIENCE

Academic Positions:

1967-69 Teaching Assistant, University of Wisconsin, Madison

1970-71 Assistant Professor, Middlebury College, Middlebury,
Vermont

1971-73 Research Instructor, California Institute of Technology,
Pasadena, California

1973-77 Assistant Professor, Kent State University

1977-87 Associate Professor, Kent State University

1987- Professor, Kent State University

Visiting Positions:

Jan-Apr-1976 Visiting Assistant Professor, University of
Pittsburgh

Apr-Sep-1977 Visiting Assistant Professor, Mathematics Research
Center, University of Wisconsin, Madison

Sep-June-1988 Visiting Scientist, T.J. Watson Research Center, I.B.M.,
Yorktown Heights, N.Y.

Consulting Positions:

Jun-Aug-1973 Consultant, IBM T.J. Watson Research Center, Yorktown
Heights, NY

Jan-Jul-1980 Research Scientist, IBM T.J. Watson Research
Center, Yorktown Heights, N.Y.

RESEARCH AWARDS, GRANTS AND FELLOWSHIPS

1967-70 NASA Traineeship

1990 NSP Grant DMS-8913209

MATHEMATICAL INTERESTS

Spline functions, numerical analysis, numerical quadrature, differential inequalities, approximation
theory, classical analysis, optimization

UNIVERSITY, PROFESSIONAL AND PUBLIC SERVICE

University:

1979-81 Served on University committees for internal review
of English and Chemistry programs.

1981-88 Director of Pi Mu Epsilon Mathematics Honorary

1984-86 Chairman, Undergraduate Studies Committee

1984-86 College Curriculum Committee, College of Arts and
Sciences

1993-95 College Advisory Committee, College of Arts and
Sciences

1996-98 Faculty Senate

1996-97 Executive Committee of the Faculty Senate

1996-98 Professional Standards Committee

Professional:

Jan-1982 Organized a Special Session on Spline Functions for AMS national winter meeting; ten
speakers from U.S.A. and Germany.

Dec-1990 Directed CBMS-NSF Conference “Curves and
Surfaces: and Algorithmic Approach.”

June-1995 Plenary address, Canadian
Mathematical Society. University of Alberta

July-2008 Conference presentation “A
context of Sylvester’s theorem on shifted monomial powers” at the

Renyi
Institute of the Hungarian National Academy of Sciences, Budapest

PUBLICATIONS

1. Solution of Landau’s problem concerning higher derivatives on
the halfline, Proceedings of an International
Conference on Constructive

Function Theory, Bulgarian Academy of
Science, Sofia, 1972, 297-308, (with I. J. Schoenberg).

2. On perfect splines of least sup-norm
on the real axis, Journal of Approximation Theory, 8(1973), 285-303, (Thesis).

3. Oscillatory and zero properties for perfect splines
and mono-splines, Journal d’Analyse,
28(1975), 41-59.

4. Korovkin sets for finitely defined
operators, Proceedings of the Austin Approximation Theory Conference, edited by
G.G. Lorentz,

Academic Press,

5. An elementary proof of Kolmogorov’s
theorem, American Mathematical Monthly, 81(1974), 480-86.

6. One-sided inequalities for the successive derivatives of a
function, Bulletin of the American Mathematical Society, 82(1976), 303-05.

7. Periodic interpolating splines and
their limits, Proceedings of the Dutch National Academy of Sciences, Indagationes Mathematicae,

Series A, 81(1978), 515-26, (with D.
J. Newman).

8. A refinement of Kolmogorov’s
inequality, Journal of Approximation Theory, 27(1979), 45-60.

9. Interpolation in the roots of unity: an extension of a theorem
of Walsh, Resultate der Mathematik, 3(1980), 155-91,

(with A. Sharma, R. S. Varga).

10. Hermite-Birkhoff interpolation in the n-th roots of unit, Trans. Amer. Math. Soc.,
259(1980), 621-28, (with A. Sharma, R. S. Varga).

11. Lacunary trigonometric interpolation on
equidistant nodes, Proceedings of the Bonn Conference on Quantitative
Approximation,

edited by R.A. DeVore
and K. Scherer, 63-80, (with A. Sharma, R. S. Varga).

12. Multivariate interpolation and the Radon transform, Mathematische Zeitschrift,
175(1980), 263-79, (with C.A. Micchelli, A. Sharma).

13. Multivariate interpolation and the Radon transofrm,
Part II: some further examples, Proceedings of the Bonn Conference on

Quantitative Approximation, edited
by R.A. DeVore and K. Scherer, 49-61, (1981), (with
C.A. Micchelli, A. Sharma).

14. On the solvability of certain systems of linear difference
equations, SIAM Journal of Mathematical Analysis, 12(1981), 833-41,

(with

15. A factorization theorem for banded matrices, Linear Algebra and Its
Applications, 39(1981), 229-45, (with

C. A. Micchelli,
P. W. Smith).

16. A theorem of J. L. Walsh, revisited, Pacific Journal of Mathematics,
118(1985), 313-322, (with A. Sharma, R. S. Varga).

17. Multivariate interpolation and the Radon transform III, Lagrange
Representation, Proceedings of the Edmonton Approximation

Theory Conference, 3 (1983), 37-52,
(with T. N. T. Goodman, C. A. Micchelli, A. Sharma).

18. An extension of a theorem of Walsh, Resultate
der Mathematik, 7 (1984),
154-163, (with H.P. Dikshit, A. Sharma).

19. Converse Results in the Walsh Theory of Equiconvergence,
Math. Modelling and Numerical Analysis, 19, (1985), 601-609,

(with A. Sharma, R. S. Varga).

20. Convergence of a class of interpolatory splines for holomorphic
functions, Journal of Approximation Theory, 46 (1986), 374-384

(with A. Sharma, J. Tzimbalario).

21. Convergence of certain polynomial interpolants
to a function defined on the unit circle, Acta Mathematica (Hungaricae), 53
(1989),

143-147 (with H. P. Dikshit, A. Sharma).

22. On lacunary interpolation for
trigonometric polynomials, Journal of Approximation and its Applications,
5(1989), 25-38 (with C.R. Selvaraj).

23. The volume of restricted moment spaces, Rendiconti

C.A. Micchelli).

24. Subdivision algorithms for curves and surfaces, Proceedings of the
International Conference on Computer Aided Geometric Design,

edited by T. Lyche,
L.L. Schumaker, Academic Press, New York, 1989,
115-153, (with C.A. Micchelli).

25. A multivariate extension of Walsh equiconvergence,
Approximation VI, edited by C.K. Chui, L.L. Schumaker
and J.D. Ward,

Academic Press, New York, 1989,
121-124, (with C.A. Micchelli and A. Sharma).

26. The total variation of the tensor product Bernstein operator, J. of
Approximation Theory, 72, (1992), 34-39, (with Meera Sitharam).

27. Walsh equiconvergence and optimal
recovery, Analysis, 12, (1992), 271-30, (with C.A. Micchelli,
A. Sharma).

28. Variation diminishing properties and convexity for the tensor
product Bernstein operator, in Functional Analysis and Operator Theory,

edited by B.S.Yadev,
D.Singh, published by Springer-Verlag,
1992, 18-33, (with A. Sharma).

29. Pyramid patches provide potential polynomial paradigms, in
Mathematical Methods in Computer Aided Geometric Design, edited by

T.Lyche
and L.L. Schumaker, Academic Press, Inc.,

30. On modified Bojanic-Shisha operators, in Aprroximation Theory, Spline
Functions and Applications, edited by S.P.Singh, Kluwer

Academic Publishers,

31. Lacunary interpolation by cosine
polynomials, Annals of Numerical Mathematics, Volume 4(1997), pp. 181-192 (with
C.R.Selvaraj,

A. Sharma).

32. Lipschitz-type
bounds for the map A
to |A| on L(H),
Linear Algebra and its Applications, Volume 360(2003), pp. 231-235 (with
Laura Smithies).

33. Optimal Recovery of Interpolation
Operators in Hardy Spaces, Advances in Computational Mathematics, Volume
24(2006), pp.131-141 (with A. Sharma)

34. The Norm of an Interpolation
Operator on H^{\infty}(D), in Frontiers in Interpolation and
Approximation, edited by N.K. Govil, et al.,

Chapman and Hall
/CRC(2006), 33-43, (with N. Fontes-Merz).

35.
A generalization of a result of G. Polya and
its application to a continuous extension of the de la Vallee
Poussin means,

to appear in Journal of
Approximation Theory, (2008) (with Terence Hanchin)

BOOKS

1. Stationary Subdivision, (with W. Dahmen,
C.A.Micchelli) Memoirs of the American Mathematics
Society, Volume 93,

number 453, Providence, Rhode
Island, l991

Ph.D. STUDENTS:

1. C.R. Selvaraj, Professor of
Mathematics, Pennsylvannia State Univerisity,
Shenango

2. Daniel Gonsor,
Research Scientist, Research Division of Boeing Corporation

3. Natasha Fontes, Professor of Mathematics,

4. Terry Hanchin (current student),
Department of Mathematics,

OTHER CONTRIBUTIONS:

1.
I contribute reviews on a regular basis to the American Mathematics
Society’s Math Reviews; on average,

two or three reviews a year.

2.
Refereeing duties for various journals, including Journal of Approximation
Theory.

3.
Department and university committee assignments, such as PhD examination
committees.

A. S. Cavaretta

Thu Mar 19 14:39:30 EST 1998