We show that the norm of the Bergman projection on L of the unit ball in C is comparable to csc(π/p) for 1 < p <∞.

We study the asymptotic of the Bergman kernel of the spin Dirac operator on high tensor powers of a line bundle.

We show that the Bergman projection does not preserve smoothness of functions in some pseudoconvex domains in the space of two complex variables.

We study when weighted composition operators Cφ,ψ acting between weighted Bergman spaces of infinite order are power bounded resp. uniformly mean ergodic.

It is shown that the formula for the Möbius pseudodistance for the annulus yields better estimates than previously known for the constant in the Bergman space maximum principle.

Preface The book is devoted to the spectral theory of commutative C *-algebras of Toeplitz operators on Bergman spaces, and its applications. For each such commutative algebra we construct a unitary operator which reduces each Toeplitz operator from this algebra to a certain multiplication operator, thus also providing its spectral type representation. This gives us a powerful research tool all...

Quasicrystals (QCs) exhibit crystallographically forbidden rotational symmetries and aperiodic long-range positional order. Three-dimensional quasicrystals, that is, icosahedral quasicrystals (i-QCs) belong to one of three commonly accepted subtypes: 1) Bergman; 2) Mackay; and 3) Tsai types, which are differentiated by their atom clusters that are also essential structural components of corresp...

We prove that a bounded operator S on La for p > 1 is compact if and only if the Berezin transform of S vanishes on the boundary of the unit disk if S satisfies some integrable conditions. Some estimates about the norm and essential norm of Toeplitz operators with symbols in BT are obtained.

We obtain several new characterizations for the standard weighted Bergman spaces Aα on the unit ball of C in terms of the radial derivative, the holomorphic gradient, and the invariant gradient.