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...

We introduce a family of weighted BMO spaces in the Bergman metric on the unit ball of C and use them to characterize complex functions f such that the big Hankel operators Hf and Hf̄ are both bounded or compact from a weighted Bergman space into a weighted Lesbegue space with possibly different exponents and different weights. As a consequence, when the symbol function f is holomorphic, we char...

Tropical varieties play an important role in algebraic geometry. The Bergman complex B(M) and the positive Bergman complex B+(M) of an oriented matroid M generalize to matroids the notions of the tropical variety and positive tropical variety associated to a linear ideal. Our main result is that if A is a Coxeter arrangement of type Φ with corresponding oriented matroid MΦ, then B (MΦ) is dual ...

We consider the focusing L2-critical half-wave equation in one space dimension i∂tu = Du− |u|u, where D denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold M∗ > 0 such that all H1/2 solutions with ‖u‖L2 < M∗ extend globally in time, while solutions with ‖u‖L2 > M∗ may develop singularities in finite time. In this paper, we first prove the ex...

A property of the Bergman projection associated to a bounded circular domain containing the origin in C^ is proved: Functions which extend to be holomorphic in large neighborhoods of the origin are characterized as Bergman projections of smooth functions with small support near the origin. For certain circular domains D, it is also shown that functions which extend holomorphically to a neighbor...

February 18, 2016 Professor Gio Batta Gori Editor, Regulatory Toxicology and Pharmacology, 525B Street, Suite 1900, San Diego, CA 92101-4495, USA. Professor Gori, We are writing on behalf of four associations to express our regret and concern regarding the comments made towards the crop protection industry in the December 2015 commentary by Bergman et al. (2015) entitled “Manufacturing Doubt Ab...

  This paper concerns the problem of robust stabilization of uncertain fractional-order non-autonomous systems. In this regard, a single input active control approach is proposed for control and stabilization of three-dimensional uncertain fractional-order systems. The robust controller is designed on the basis of fractional Lyapunov stability theory. Furthermore, the effects of model uncertai...

In this paper, we propose a generalization of the S-duality of four-dimensional quantum electrodynamics (QED 4 ) to QED 4 with fractionally charged excitations, the fractional S-duality. Such QED 4 can be obtained by gauging the U(1) symmetry of a topologically ordered state with fractional charges. When time-reversal symmetry is imposed, the axion angle (θ) can take a nontrivial but still time...

This paper surveys a large class of nonlinear extremal problems in Hardy and Bergman spaces. We discuss the general approach to such problems in Hardy spaces developed by S. Ya. Khavinson in the 1960s, but not well known in the West. We also discuss the major difficulties distinguishing the Bergman space setting and formulate some open problems.

In this paper we will discuss local coordinates canonically corresponding to a Kähler metric. We will also discuss the C ∞ convergence of Bergman metrics following Tian's result on C 2 convergence of Bergman metrics. At the end we present an interesting characterization of ample line bundle that could be useful in arithmetic geometry.