Mid Sweden University

In this note we prove a product property for the pluricomplex energy, and then give some applications.

Let p>0, and let

denote the cone of negative plurisubharmonic functions with finite pluricomplex p-energy. We prove that the vector space

, with the vector ordering induced by the cone

is σ-Dedekind complete, and equipped with a suitable quasi-norm it is a non-separable quasi-Banach space with a decomposition property with control of the quasi-norm. Furthermore, we explicitly characterize its topological dual. The cone

in the quasi-normed space

is closed, generating, and has empty interior.

We prove in this paper an inequality for the beta function, and we give an application in pluripotential theory.

The energy class S, is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of F, and its pluricomplex p-energy is proved.

Let D-j be a bounded hyperconvex domain in C-nj and set D = D-1 x ..... x D-s, j = 1,...,s, s >= 3. Also let G(n) be the symmetrized polydisc in C-n, n >= 3. We characterize those real-valued continuous functions defined on the boundary of D or G. which can be extended to the inside to a pluriharmonic function. As an application a complete characterization of the compliant functions is obtained.

The Cegrell classes with zero boundary data are defined by certain decreasing approximating sequences of functions with different properties depending on the class in question. It is different for Cegrell classes which are given by a continuous function f, these classes are defined by an inequality. It is proved in this article that it is possible to define the Cegrell classes which are given by f in a similar manner as those classes with zero boundary data. An existence result for the Dirichlet problem for certain singular measures is proved. The article ends with three applications. Results connected to convergence in capacity, subextension of plurisubharmonic functions and integrability are proved.

Let $mathcal{P}$ be a connected, non-degenerate analytic polyhedron in $mathbb{C}^n$, $ngeq 2$. In this note we characterize those continuous functions which can be extended to a plurisubharmonic function in $mathcal{P}$.

In multi-carrier modulation systems such as OFDM, several subcarriers are used for transmission and their received signal quality is different from one subcarrier to others in frequency selective fading channel. In this paper an enhanced hybrid ARQ scheme for OFDM systems is proposed. When data is requested for retransmissions, we change the bit interleaving mode in such manner that the data sequence is changed. Since the coded bit is assigned to different subcarriers and positions of a modulation symbols in different retransmissions we can take advantage of this effect, and achieve both frequency- and modulation constellation diversity. Results from computer simulations confirm that the proposed scheme improves the throughput performance. After two transmissions and with packet error rate (PER) of 10(-4) the proposed scheme gain approximate 3 dB compared to a scheme emploving Chase combining. The performance gain is even more for three transmissions (2 retransmissions).