Electronic Resource
Springer
Integral equations and operator theory
7 (1984), S. 145-205
ISSN:
1420-8989
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The interplay between the theory of Toeplitz operators on the circle and the theory of pseudodifferential operators on the line (i. e. Wiener-Hopf operators) is by now well-known and well-understood. In this article we show that there is a parallel situation in higher dimensions. To begin with, by using pseudodifferential multipliers, one can simplify the composition rules for Toeplitz operators, (§ 3), and describe precisely how Toeplitz operators of “Bergmann type” are related to Toeplitz operators of “Szegö type” (§ 9). Furthermore, it turns out that the ring of pseudodifferential operators on a compact manifold, M, is isomorphic with the ring of Toeplitz operators on an appropriate Grauert tube about M (§ § 4–6), and the ring of Weyl operators on ℝn is isomorphic with the ring of Toeplitz operators on the complex ball in ℂn (§ § 7–10).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01200373
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