Inhaltsverzeichnis - Mathematisches Institut der Universität zu Köln

DMV Tagung 2011 - Köln, 19. - 22. September
Wolfram Bauer
Georg-August-Universität, Göttingen
Algebraic properties and the finite rank problem for Toeplitz operators
We address three different problems in the area of Toeplitz operators on the Segal-Bargmann space
over C n . First, we determine the commutant of a given Toeplitz operator with radial symbol which has a
controlled growth behaviour at infinity. Then we provide explicit examples of zero-products of non-trivial Toeplitz
operators. These examples show the essential difference between Toeplitz operators on the Segal-
Bargmann space and on the Bergman space over the unit ball. Finally, we discuss the ”finite rank problem”
in the setting of an unbounded domain. In all these problems the growth at infinity of the operator symbol
plays a crucial role. The results presented in this talk are joint work with Trieu Le, University of Toledo.
Literatur
W. Bauer, T. Le. Algebraic properties and the finite rank problem for Toeplitz operators on the Segal-
Bargmann space, preprint, (2011).
W. Bauer, Y.L. Lee. Commuting Toeplitz operators on the Segal-Bargmann space, J. Funct. Anal., 260,
460-489, (2011).
T. Le. The commutants of certain Toeplitz operators on weighted Bergman spaces, J. Math. Anal. Appl.,
348(1), 1-11, (2008).
D. Luecking. Finite rank Toeplitz operators on the Bergman space, Proc. Amer. Math. Soc., 136(5), 1717-
1723, (2008).
Swanhild Bernstein
TU Bergakademie Freiberg
Inverse Scattering with Dirac Operators
We develop a reconstruction scheme of the potential from the scattering matrix of the Dirac operator by
using Faddeev’s method for the multi-dimensional inverse scattering theory for Schrödinger operators.
We also demonstrate how Dirac operators can be used to construct Lax pairs for linear and non-linear
systems of partial differential equations. Further, we construct Lax pairs using the AKNS method for a
higher dimensional version of the nonlinear KdV equation.
Literatur
Hiroshi, I. (1997). Inverse scattering theory for Dirac operators. Ann. Inst. Henri Poincaré, 66(2), 237-270.
Fokas, A. S. (1997). A modified transform method for solving linear and some nonlinear PDEs. Proc. Royal
Soc. London A, 453, 1411-1443.
Aktosun, T. (2004). Inverse Scattering Transform, KdV, and Solitons, In: J.A. Ball, J.W. Helton, M. Klaus
and L. Rodman (eds), Current trends in operator theory and its applications, Operator theory: Advances
and Applications, 149, Birkhäuser Basel, 1-22.
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