In this paper we describe the suitability of hierarchically S-decomposable fuzzy measures for combining information. In particular, they are adequate when the set of information sources include some redundant sources and also some complementary ones. We show how these two types of sources can be combined in a single aggregation operator. Besides of that, we show how the measures allow modularit...

Sobolev orthogonal polynomials with respect to measures supported on subsets of the complex plane are considered. The connection between the following properties is studied: the multiplication operator M p(z) = zp(z) defined on the space P of algebraic polynomials with complex coefficients is bounded with respect to the norm defined by the Sobolev inner product, the supports of the measures are...

It is shown that any convolution operator in the time domain can be represented exactly as a multiplication operator in the time-scale (wavelet) domain. The Mellin transform gives a one-to-one correspondence between frequency filters (system functions) and scale filters (multiplication operators in the scale domain), subject to the convergence of the defining integrals. The usual wavelet recons...

We review the probabilistic properties of Ornstein-Uhlenbeck processes in Hilbert spaces driven by Lévy processes. The emphasis is on the different contexts in which these processes arise, such as stochastic partial differential equations, continuous-state branching processes, generalised Mehler semigroups and operator self-decomposable distributions. We also examine generalisations to the case...

Let G be a semisimple Lie group, g its Lie algebra. For any symmetric space M over G we construct a new (deformed) multiplication in the space A of smooth functions on M. This multiplication is invariant under the action of the Drinfeld–Jimbo quantum group U h g and is commutative with respect to an involutive operator˜S : A⊗A → A⊗A. Such a multiplication is unique. Let M be a kählerian symmetr...

In this article, we shall discuss some recent developments and applications of the local spectral theory for linear operators on Banach spaces. Special emphasis will be given to those parts of operator theory, where spectral theory, harmonic analysis, and the theory of Banach algebras overlap and interact. Along this line, we shall present the recent progress of the theory of quotients and rest...

Genetic algorithms (GAs) are useful in the eld of continuous parameter optimization. Many results indicate that, due to their robust-ness and their ability of escaping from local optima, GAs are especially suitable for optimizing multimodal functions that contain millions of misleading local optima. The existing theory is based on spherical symmetric functions and suggest an O(n ln n) complexit...

In the present paper we study a relation between the Lorentzian twistor equation and CR-geometry. Besides the Dirac operator there is a second important conformally covariant differential operator acting on the spinor fields Γ(S) of a smooth semiRiemannian spin manifold (M,g) of dimension n and index k, the so-called twistor operator D. The twistor operator is defined as the composition of the ...

A multiplication operator on a Hilbert space may be approximated with finite sections by choosing an orthonormal basis of the Hilbert space. Nonzero multiplication operators on L spaces of functions are never compact and then such approximations cannot converge in the norm topology. Instead, we consider how well the spectra of the finite sections approximate the spectrum of the multiplication o...