Anzeige
Erschienen in:
2008 | OriginalPaper | Buchkapitel
Dynamics of Properties of Toeplitz Operators with Radial Symbols
Erschienen in: Commutative Algebras of Toeplitz Operators on the Bergman Space
Verlag: Birkhäuser Basel
Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.
Wählen Sie Textabschnitte aus um mit Künstlicher Intelligenz passenden Patente zu finden. powered by
Markieren Sie Textabschnitte, um KI-gestützt weitere passende Inhalte zu finden. powered by
Given a smooth defining symbol
a=a(z)
, the family of Toeplitz operators
$$ T_a = \left\{ {T_a^{\left( h \right)} } \right\} $$
, where
h
∈(0, 1), was considered in the previous chapter under the Berezin quantization procedure. For a fixed
h
the Toeplitz operator
T
a
(h)
acts on the weighted Bergman space
$$ \mathcal{A}_h^2 \left( \mathbb{D} \right) $$
, where the parameter
h
characterizes the weight (10.1.5) on
$$ \mathcal{A}_h^2 \left( \mathbb{D} \right) $$
. In the sequel we will consider another form of presentation of the weighted Bergman spaces, see (10.1.1), the space
$$ \mathcal{A}_\lambda ^2 \left( \mathbb{D} \right) $$
which is parameterized by λ∈(−1, +∞) being connected with
h
∈(0, 1) by the rule
$$ \lambda + 2 = \frac{1} {h} $$
, see Section 10.1.