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


1966 B.A.   Mathematics, Dartmouth College, Hanover, NH
1968 M.A.
  Mathematics, University of Wisconsin, Madison
1970 Ph.D.
  University of Wisconsin, Madison


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.


1967-70 NASA Traineeship
1990       NSP Grant DMS-8913209


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


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

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


   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, New York, 1973, 299-307.
   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 W. Dahmen, C. A. Micchelli, P. W. Smith).
  15. A factorization theorem for banded matrices, Linear Algebra and Its Applications, 39(1981), 229-45, (with W. Dahmen,
        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 del Circolo Matematico di Palermo, 38(1989), 419-429, (with W. Dahmen,
        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., New York, 1992, 69-100, (with C.A.Micchelli).
  30. On modified Bojanic-Shisha operators, in Aprroximation Theory, Spline Functions and Applications, edited by S.P.Singh, Kluwer
        Academic Publishers, Dordrecht, 1992, 303-310, (with S.S.Guo).
  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)


   1. Stationary Subdivision, (with W. Dahmen, C.A.Micchelli) Memoirs of the American Mathematics Society, Volume 93,
        number 453, Providence, Rhode Island, l991


   1. C.R. Selvaraj, Professor of Mathematics, Pennsylvannia State Univerisity, Shenango
   2. Daniel Gonsor, Research Scientist, Research Division of Boeing Corporation
Natasha Fontes, Professor of Mathematics, Westminster College, Westminster Pennsylvannia
  Terry Hanchin  (current student), Department of Mathematics, Kent State University


   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