Evolving Art) ft Yet the film is an Important one if for no other reason than that It allows us a glimpse of Bergman as an evolving film artist. It allows us a splendid opportunity to see that fluid style, mastery of the camera and ingenious power of creating mood that have made Bergman one of the mosthighly lauded directors in the history of film, In f The Naked Night" Mr. Bergman explores the...

I have recently shown that the Bergman kernel associated to a finitely connected domain in the plane is given as an explicit rational combination of finitely many basic functions of one complex variable. In this paper, it is proved that all the basic functions and constants in the new formula for the Bergman kernel can be evaluated using one-dimensional integrals and simple linear algebra. In f...

We show that under mild conditions, a Gaussian analytic function F that a.s. does not belong to a given weighted Bergman space or Bargmann–Fock space has the property that a.s. no non-zero function in that space vanishes where F does. This establishes a conjecture of Shapiro (1979) on Bergman spaces and allows us to resolve a question of Zhu (1993) on Bargmann–Fock spaces. We also give a simila...

Let L be an ample line bundle on a (geometrically reduced) projective variety X over any complete valued field. Our main result describes the leading asymptotics of determinant cohomology large powers L, with respect to supnorm continuous metric Berkovich analytification L. As consequence, we establish in this setting existence transfinite diameters and equidistribution Fekete points, following...

We investigate a vector-valued version of the classical continuous wavelet transform. Special attention is given to the case when the analyzing vector consists of the first elements of the basis of admissible functions, namely the functions whose Fourier transform is a Laguerre function. In this case, the resulting spaces are, up to a multiplier isomorphism, poly-Bergman spaces. To demonstrate ...

Let ϕ be a real-valued plurisubharmonic function on [Formula: see text] whose complex Hessian has uniformly comparable eigenvalues, and let [Formula: see text] be the Fock space induced by ϕ. In this paper, we conclude that the Bergman projection is bounded from the pth Lebesgue space [Formula: see text] to [Formula: see text] for [Formula: see text]. As a remark, we claim that Bergman projecti...

In order to find explicit numerical approximation of Kähler-Einstein metric of projective manifolds, Donaldson introduced in [3] various operators with good properties to approximate classical operators. See the discussions in Section 4.2 of [3] for more details related to our discussion. In this note we verify certain statement of Donaldson about the operator QK in Section 4.2 by using the ful...

We consider the weighted Bergman spaces HL(B, μλ), where we set dμλ(z) = cλ(1−|z| 2) dτ (z), with τ being the hyperbolic volume measure. These spaces are nonzero if and only if λ > d. For 0 < λ ≤ d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. S...

We give various equivalent formulations to the (partially) open problem about Lboundedness of Bergman projections in tubes over cones. Namely, we show that such boundedness is equivalent to the duality identity between Bergman spaces, A ′ = (Ap)∗, and also to a Hardy type inequality related to the wave operator. We introduce analytic Besov spaces in tubes over cones, for which such Hardy inequa...

We show that the approximation numbers of a compact composition operator on the weighted Bergman spaces Bα of the unit disk can tend to 0 arbitrarily slowly, but that they never tend quickly to 0: they grow at least exponentially, and this speed of convergence is only obtained for symbols which do not approach the unit circle. We also give an upper bounds and explicit an example. Mathematics Su...