Ognyan Kounchev
I was
Visiting Professor, Fulbright
Fellow
Wavelet
IDR Center,
Department of Computer Sciences, University of Wisconsin – Madison
Address:
Department
of Computer Sciences, The Wavelet
IDR Center,
University
of Wisconsin – Madison, 1210 W. Dayton St., Madison, WI 537061380;
t.n. (608)
2626612
email addresses:
kounchev@cs.wisc.edu;
kounchev@math.unidusiburg.de;
kounchev@cblink.net;
kounchev@emath.ams.org;
Monograph, appeared in June 2001:
See some chapters: Table of Contents,
Chapter 1 which is the Introduction; Chapter
6 containing applications of the polysplines to magnetic
data and to CAGD data, Chapter 13
which contains an exposition of the Micchelli's theory of cardinal Lsplines,
and Chapter 16 containing a brief
review of Chui's cardinal spline wavelet analysis.
Awards
Alexander
von HumboldtFoundation – Research Grant, 1992
Fulbright
Commission  Research Scholarship, 2000
Professional
Experience
1999:VisitingProfessor–
Institute for Applied Mathematics, University of Hamburg, Germany
19961998:Visiting
by a Project"The Polyharmonicity Concept in Constructive Theory of Functions"
with
the Volkswagen
Foundation (Hannover)
– Department of Mathematics,University of Duisburg
1997:VisitingProfessor,
Institute for Applied Mathematics, University of Hamburg, Germany
1994,
1995:Visiting Research Professor by projects with the Max
Planck Society
– WG of the Max Planck Society, Department of Mathematics,University of
Potsdam
19921994:
Grant from the Alexander
von Humboldt Foundation
(Bonn) – Department of Mathematics, University of Duisburg
1991:Visiting
Associate Professor, Northwestern University, Evanston, USA
1995:Associate
Professor, Institute of Mathematics, Bulgarian Academy of Sciences
19841995:Assistant
Professor, Institute of Mathematics, Bulgarian Academy of Sciences
Selected Publications (with reference to Math. Reviews if
available)

Haußmann, Werner;
Kounchev, Ognyan, Definiteness of the Peano kernel associated with the
polyharmonic mean value property. J. London Math. Soc. (2) 62 (2000),
no. 1, 149160.

Haußmann, Werner; Kounchev, Ognyan,
Peano Kernel associated with the polyharmonic mean value property in the
annulus, to appear in Numer. Funct. Anal. and Optimization.

99j:65003 Dryanov, Dimiter; Kounchev, Ognyan, Polyharmonically exact formula
of EulerMaclaurin,multivariate Bernoulli functions, and Poisson type formula.
C. R. Acad. Sci. Paris Sér. I Math. 327 (1998), no. 5, 515520.

98h:41038 Kounchev, Ognyan Iv., Minimizing the Laplacian of a function
squared with prescribed values on interior boundariestheory of polysplines.
Trans. Amer. Math. Soc. 350 (1998), no. 5, 21052128.

98f:41030 Haußmann, Werner; Kounchev, Ognyan, Peano theorem for linear
functionals vanishing on polyharmonic functions. In: Approximation theory
VIII, Vol. 1 (College Station, TX, 1995), 233240, Ser. Approx. Decompos.,
6, World Sci. Publishing, River Edge, NJ, 1995.

96f:41010 Kounchev, O., Optimal recovery of linear functionals of Peano
type through data on manifolds. Concrete analysis. Comput. Math. Appl.
30 (1995), no. 36, 335351.

Kounchev, O. I. Splines constructed by pieces of polyharmonic functions.
In: Wavelets, images, and surface fitting (ChamonixMontBlanc,
1993), 319326, A K Peters, Wellesley, MA, 1994.

93h:41019 Kounchev, O. I. Harmonicity modulus and applications to the approximation
by polyharmonic functions. In: Approximation by solutions of partial
differential equations (Hanstholm, 1991), 111125, NATO Adv. Sci.
Inst. Ser. C Math. Phys. Sci., 365, Kluwer Acad. Publ., Dordrecht, 1992.

O. Kounchev: Problems
in multivariate constructive function theory. In: Approximation by Solutions
of Partial Differential Equations, Eds. B. Fuglede et al., Kluwer,
1992, pp. 198200.

93a:41016 Kounchev, O. Iv. Definition and basic properties of polysplines.
C. R. Acad. Bulgare Sci. 44 (1991), no. 7, 911.

92m:41031 Kounchev, O. I. Basic properties of polysplines, II. C. R.
Acad. Bulgare Sci. 44 (1991), no. 8, 1316.

92j:35042b Kounchev, Ognyan Iv. Sharp estimate of the Laplacian of a polyharmonic
function and applications. Trans. Amer. Math. Soc. 332 (1992), no.
1, 121133.

O. Kounchev: The
elliptical current loop model of Earth's magnetic and paleomagnetic field
sources. In: Geophysical Data Inversion. Methods and Applications,
Ed. A. Vogel et al., Friedrich Vieweg and Son, 1990, pp. 129148.

O. Kounchev: Solving
inverse problems for potential fields for nonuniform data with error. In:
Theory and Practice of Geophysical Data Inversion, Friedrich Vieweg
and Son, 1990, pp. 109119.

90f:31007 Kounchev, Ognyan, Extremal problems for the distributed moment
problem. In: Potential theory (Prague, 1987), 187195, Plenum,
New YorkLondon, 1988.

O. Kounchev: Uniform
Approximation by harmonic functions. Math. Series of the University
of Greifswald, No. 4, 1989, pp. 5053.

O. Kounchev: Obtaining
Materic Bodies through concentration and optimization of a linear functional.
In: Geophysical Data Inversion. Methods and Applications, Ed. A.
Vogel et al., Friedrich Vieweg and Son, 1990, pp. 129148.

88k:30045 Kounchev, O. Iv. On the uniform approximation of a continuous
function by analytic functions a Chebyshev criterion. In: Complex analysis
and applications '85 (Varna, 1985), 367377, Bulgar. Acad. Sci., Sofia,
1986.
Research Interests

Partial Differential
Equations, Potential Theory and Applications to Inverse problems in Geophysics
and Geomagnetism;

Applications of
solutions of higher order elliptic equations (in particular polyharmonic
and polyanalytic functions) to Multivariate Constructive Theory of Functions
– Approximation Theory, Spline Theory, Moment Problems and Orthogonality;

Harmonic Analysis
and especially Wavelet Analysis;

Multivariate orthogonality,
Padé
approximations with applications to Inverse Problems in Spectral Theory,
and Operators in Hilbert space with infinite multiplicity, in particular
Schroedinger operators;

Elliptic BVP in
domains with singularities;
Currently lecturing:
During the fall semester
of the year 2000, a series of lectures on “Multivariate Polysplines and
Applications to Numerical and Wavelet Analysis” at the Seminar on Approximation
Theory, Monday 45pm,Computer Sciences, seminar room CS5331.
Last update: October 1, 2000.