Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

On the existence of eigenvalues of Toeplitz operators on planar regions


Authors: Cyrus P. Aryana and Kevin F. Clancey
Journal: Proc. Amer. Math. Soc. 132 (2004), 3007-3018
MSC (2000): Primary 47B35
DOI: https://doi.org/10.1090/S0002-9939-04-07273-9
Published electronically: June 2, 2004
MathSciNet review: 2063122
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: A study is made of the eigenvalues of self-adjoint Toeplitz operators on multiply connected planar regions having $g$ holes. The presence of eigenvalues is detected through an analysis of the zeros of translations of theta functions restricted to $\mathbb{R}^{g}$ in $\mathbb{C}^{g}$.


References [Enhancements On Off] (What's this?)

  • [1] M. B. Abrahamse, Toeplitz operators in multiply connected regions, Amer. Jour. Math. 96 (1974), 261-297. MR 50:14333
  • [2] G. Akbari Estahbanati (Cyrus P. Aryana), Riemann surfaces and Toeplitz operators on multiply connected planar regions, Dissertation, University of Georgia, 1993.
  • [3] K. F. Clancey, Toeplitz operators on multiply connected domains and theta functions, Operator Theory: Adv. and Appl. 35 (1988), 311-355. MR 91f:47038
  • [4] K. F. Clancey, On the spectral character of Toeplitz operators on multiply connected domains, Trans. Amer. Math. Soc., vol. 323 (1991), 897-910.MR 91f:47039
  • [5] K. F. Clancey, Representing measures on multiply connected planar domains, Illinois J. Math., vol. 35 (1991), 286-311. MR 92e:46110
  • [6] H. M. Farkas and I. Kra, Riemann Surfaces, Springer-Verlag, New York, 1992.MR 93a:30047
  • [7] J. D. Fay, Theta Functions on Riemann Surfaces, Lecture Notes in Mathematics No. 352, Springer-Verlag, New York, 1973. MR 49:569
  • [8] J. D. Pincus and J. Xia, Symmetric and self-adjoint Toeplitz operators on multiply connected planar domains, J. Funct. Anal. 59 (1984), 397-444. MR 87i:47038

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47B35

Retrieve articles in all journals with MSC (2000): 47B35


Additional Information

Cyrus P. Aryana
Affiliation: Department of Mathematical Sciences, Saginaw Valley State University, University Center, Michigan 48710
Email: aryana@svsu.edu

Kevin F. Clancey
Affiliation: Department of Mathematics, University of Louisville, Louisville, Kentucky 40292
Email: k.clancey@louisville.edu

DOI: https://doi.org/10.1090/S0002-9939-04-07273-9
Keywords: Double, harmonic measure, theta function, Hardy space, Toeplitz operator
Received by editor(s): June 5, 2002
Received by editor(s) in revised form: March 7, 2003
Published electronically: June 2, 2004
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2004 American Mathematical Society

American Mathematical Society