In this paper we study the Hilbert space of analytic functions with finite Dirichlet integral in a connected open set C2 in the complex plane. We show that every such function can be represented as a… (More)

// A A’ (1 < E, (1 B B’ (1 < C. (3) Furthermore, if B is self-adjoint then B’ can be chosen to be self-adjoint also. Note the asymmetry in (3), with strict inequality for one term but not for the… (More)

The principal question with which this paper is concerned is the following: if a manifold M admits a continuous associative multiplication with identity and no other idempotents, is it a group? We… (More)

We demonstrate that single photons can be generated from single InAs/GaAs quantum dots in photolithographically defined pillar microcavities. Pillars with a 1.9 microm diameter cavity show a four… (More)

This result was conjectured by A. E. Taylor in 1951 (see [7, p. 33]). The analogous proposition for two-sided sequences { • • • , a_i, a0, ai, ■ ■ ■ }, with the space H°> of bounded analytic… (More)

For example, Theorem 3 says that if V is a closed subspace of f2 and if V CQp for some p < 2, then V is finite-dimensional . On the other hand, the corollary to Theorem 4 states that there exist… (More)

Let H denote a separable, infinite-dimensional Hilbert space. We shall consider operators (that is, bounded linear transformations) on/-/. An operator T is said to be in the Schatten class Cp if T is… (More)

Since a compact manifold which admits a continuous, associative multiplication with identity must be a group [l], the two-sphere cannot be a (topological) semigroup with identity. S. T. Hu has raised… (More)

The proofs use the notion of analytic structure in a maximal ideal space. J. Wermer first obtained results along these lines and further contributions were made by E. Bishop and H. Royden and then by… (More)