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 Szegő kernel of an annulus

Authors: Scott McCullough and Li-Chien Shen
Journal: Proc. Amer. Math. Soc. 121 (1994), 1111-1121
MSC: Primary 30C40; Secondary 46E22
MathSciNet review: 1189748
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In this paper we introduce a class of reproducing kernels of an annulus. Using the properties of the theta functions, we obtain a set of functional equations involving these kernels. We discuss some extremal problems associated with the functional equations.

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

  • [1] M. B. Abrahamse, The Pick interpolation theorem for finitely connected domains, Michigan Math. J. 26 (1979), 195-203. MR 532320 (80j:30052)
  • [2] M. B. Abrahamse and R. G. Douglas, A class of subnormal operators related to a multiply connected domain, Adv. Math. 121 (1976), 106-108. MR 0397468 (53:1327)
  • [3] J. Agler, Rational dilation on an annulus, Ann. of Math. (2) 121 (1985), 537-564. MR 794373 (87a:47007)
  • [4] J. A. Ball and K. F. Clancey, Reproducing kernels for Hardy spaces on multiply connected domains, preprint. MR 1386327 (97f:46042)
  • [5] S. Bergman, The kernel function and conformal mapping, Amer. Math. Soc. Survey 5 (1950). MR 0038439 (12:402a)
  • [6] John D. Fay, Theta functions on Riemann surfaces, Lecture Notes in Math., vol. 352, Springer, New York, 1973, p. 352. MR 0335789 (49:569)
  • [7] G. Misra, Curvative inequalities and extremal properties of bundle shifts, J. Operator Theory 11 (1984), 305-318. MR 749164 (86h:47057)
  • [8] Z. Nehari, Conformal mapping, Dover, New York, 1985. MR 0377031 (51:13206)
  • [9] V. I. Paulsen, Completely bounded maps and dilations, Pitman Press, New York, 1986. MR 868472 (88h:46111)
  • [10] D. Sarason, The $ {H^p}$ spaces of an annulus, Mem. Amer. Math. Soc., vol. 56, Amer. Math. Soc., Providence, RI, 1975. MR 0188824 (32:6256)
  • [11] E. T. Whittaker and G. N. Watson, A course of modern analysis, 4th ed., Cambridge Univ. Press, New York, 1958. MR 1424469 (97k:01072)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C40, 46E22

Retrieve articles in all journals with MSC: 30C40, 46E22

Additional Information

Article copyright: © Copyright 1994 American Mathematical Society

American Mathematical Society