It is shown that sets of sampling for the Bergman space A2 have the “homogeneous approximation property” (HAP) and that sets with this property are sampling for A 2+E. In addition, previous results concerning the boundary behaviour of sampling sets are improved. ForO<p<oo, the Bergman space AP is the set of functions f analytic in the unit disk D = (2 : 1.~1 < 1) with where dA denotes Lebesgue ...

Let D be a bounded domain in C". The invariant distance in D is given by I I v I \ is l \\ '/2\ l/2 Kp(z,i)K„(w,w) It is shown that one half of the length of a piecewise C1 curve y: [a, b] -* D with respect to the Bergman metric is equal to the length of y measured by pD, which implies that the associated inner distance p*D coincides (up to the factor {) with the Bergman-distance. Also it was p...

The Fredholm properties of Toeplitz operators on the Bergman space A have been well-known for continuous symbols since the 1970s. We investigate the case p = 1 with continuous symbols under a mild additional condition, namely that of the logarithmic vanishing mean oscillation in the Bergman metric. Most differences are related to boundedness properties of Toeplitz operators acting on A that ari...

We study the condition that characterizes the symbols of bounded Hankel operators on the Bergman space of a strongly pseudoconvex domain and show that it is equivalent to BMO plus analytic. (Here we mean the Bergman metric BMO of Berger, Coburn and Zhu.) In the course of the proof we obtain new d -estimates that may be of independent interest. Some applications include a decomposition of BMO si...

We quantise complex, infinite–dimensional projective space CP(H). We apply the result to quantise a complex, finite–dimensional, classical phase space C whose symplectic volume is infinite, by holomorphically embedding it into CP(H). The embedding is univocally determined by requiring it to be an isometry between the Bergman metric on C and the Fubini–Study metric on CP(H). Then the Hilbert–spa...