ii

We consider the hyperbolic Hardy class %Hp(B), 0 < p < ∞. It consists of φ holomorphic in the unit complex ball B for which |φ| < 1 and sup 0<r<1 ∫ ∂B {%(φ(rζ), 0)} dσ(ζ) < ∞, where % denotes the hyperbolic distance of the unit disc. The hyperbolic version of the Littlewood-Paley type g-function and the area function are defined in terms of the invariant gradient of B, and membership of %Hp(B) ...

We give a new and simple compactness criterion for composition operators Cφ on BMOA and the Bloch space in terms of the norms of φ in the respective spaces.

In this paper we use Hodge theory to define a filtration on the Chow groups of a smooth, projective algebraic variety. Assuming the generalized Hodge conjecture and a conjecture of Bloch-Beilinson, we show that this filtration terminates at the codimension of the algebraic cycle class, thus providing a complete set of period-type invariants for a rational equivalence class of algebraic cycles. ...

We present a formula for the full Cheeger-Chern-Simons class of the tautological flat complex vector bundle of rank 2 over BSL(2, C). Our formula improves the formula in [DZ], where the class is only computed modulo 2-torsion.

Motivated by Harish-Chandra theory, we construct, starting from a simple CDD-pole S-matrix, a hierarchy of new S-matrices involving ever “higher” (in the sense of Barnes) gamma functions. These new S-matrices correspond to scattering of excitations in ever more complex integrable models. From each of these models, new ones are obtained either by “q-deformation”, or by considering the Selberg-ty...

Let H(B) be the space of all holomorphic functions on the unit ball B in CN , and S(B) the collection of all holomorphic self-maps of B . Let φ ∈ S(B) and g ∈ H(B) with g(0) = 0 , the generalized composition operator is defined by C φ ( f )(z) = ∫ 1 0 R f (φ(tz))g(tz) dt t , Here, we characterize the boundedness and compactness of the generalized composition operator acting from Bloch-type spac...

A method is presented for solving the Bloch equation for Morse potential, based on the application of Fourier transformation of the density matrix. The results obtained agree completely with the results obtained by other methods, however its advantage lies in its elegance and intuitivity of the approach. q 2000 Elsevier Science Ltd. All rights reserved.

Imbed a n w 1 sphere in an n sphere, and the complement is divided into two components. I t seems that the closure of each of the resulting components should be a topological w-cell. This statement isn't true. The classical counterexample (in dimension 3) is the Alexander Horned Sphere. I t was conjectured, however, that if one restricts one's attention to some class of well-behaved imbeddings,...

Assuming the Bloch-Kato Conjecture, we determine precise conditions under which Hilbert 90 is valid for Milnor k-theory and Galois cohomology. In particular, Hilbert 90 holds for degree n when the cohomological dimension of the Galois group of the maximal p-extension of F is at most n.