E. Ramírez de Arellano

Algebras of singular integral operators generated by three orthogonal projections

The structure of theC*-algebra with identity generated by two orthogonal projections is well understood. All irreducible representations of this algebra are either two-dimensional or one-dimensional. The situation becomes unpredictable in the case of theC*-algebra generated by three orthogonal projections. Even in the more specific case when two of the projections commute, the algebra under consideration may have infinite dimensional irreducible representations.In this paper we produce three concrete realizations of the algebra generated by three orthogonal projections in that specific case. It turns out that these algebras have quite different structure.

Hyperbolic Systems with Multiplicity Greater Than or Equal to Three

The wave propagation for nonstrictly hyperbolic systems whose principal symbol has a Jordan block is considered.

Complex analysis and related topics

Local integrability of systems of m smooth linearly independent complex vector fields on m + 1 dimensional manifolds, Lilia N. Apostolova on asymptotic properties of the one-dimensional Schrodinger equation, Irina V. Astashova on Qp functions, Rauno Aulaskari on Greens functions for subelliptic operators, Richard Beals et al Clifford analysis on Poincare space, Jan Cnops unitarity invariant trace extensions beyond the trace class, K. Dykema et al Lie superalgebras of supermatrices of complex size - their generalizations and related integrable systems, P. Grozmman, D. Leites a new local variant of the Hausdorff-Young inequality, Amir Kamaly a survey of Qp spaces, Peter Lappan Hurwitz-type and space-time-type duality theorems for Hermitian Hurwitz pairs, Julian Lawrynowicz, Osamu Suzuki on the problem of deciding whether a holomorphic vector field is complete, Jorge L. Lopez, Jesus Mucino-Raymundo variations on a theorem of Severi, D. Napoletani et al Bergman-Toeplitz and pseudo-differential operators, V. Rabinovich, N. Vasilevski the small Hankel operator in several complex variables, Bernard Russo the reproducing kernel Hilbert space and its multiplication operators, Franciszek Hugon Szafraniec Lie algebras in Fock space, A. Turbiner. (Part contents).

On Integral Representations and Boundary Properties of Spinor Fields

A new approach to the boundary value problem for the classic Dirac equation is proposed. This approach is based on a recent version of the metaharmonic quaternionic analysis developed in [14-16]. In particular, the following problem is studied: when and how a given function on a surface can be extended to a time-harmonic spinor field.

Fueter - hurwitz regular mappings and an integral representation

An index formula is defined and it is used to derive a sufficiently general Cauchy integral formula for regular mappings in the euclidean Hurwitz pairs theory. Such a formula is a generalisation of the standard one known from the complex analysis.