Advertisement

Toeplitz Operators on the Upper Half-Plane with Homogeneous Symbols

Part of the Operator Theory: Advances and Applications book series (OT, volume 185)

Abstract

In this chapter we return to the upper half-plane Π, the space L2(Π) and its Bergman subspace A2(Π). Passing to polar coordinates we have
$$ L_2 \left( \prod \right) = L_2 \left( {\mathbb{R}_ + ,rdr} \right) \otimes L_2 \left( {\left[ {0,\pi } \right],d\theta } \right) = L_2 \left( {\mathbb{R}_ + ,rdr} \right) \otimes L_2 \left( {0,\pi } \right), $$
and
$$ \frac{\partial } {{\partial \bar z}} = \frac{{\cos \theta + i\sin \theta }} {2}\left( {\frac{\partial } {{\partial r}} + i\frac{1} {r}\frac{\partial } {{\partial \theta }}} \right) = \frac{{\cos \theta + i\sin \theta }} {{2r}}\left( {r\frac{\partial } {{\partial r}} + i\frac{\partial } {{\partial \theta }}} \right). $$

Keywords

Boundary Point Compact Operator Toeplitz Operator Local Algebr Bergman Projection 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Birkhäuser Verlag AG 2008

Personalised recommendations