Analysis and Applications - ISAAC 2001

This collection of survey articles gives and idea of new methods and results in real and complex analysis and its applications. Besides several chapters on hyperbolic equations and systems and complex analysis, potential theory, dynamical systems and harmonic analysis are also included. Newly developed subjects from power geometry, homogenization, partial differential equations in graph structures are presented and a decomposition of the Hilbert space and Hamiltonian are given.
Audience: Advanced students and scientists interested in new methods and results in analysis and applications.

Klappentext

The 3rd International ISAAC Congress took place from August 20 to 25, 2001 in Berlin, Germany, supported by the German Research Foundation (DFG), the city of Berlin through Investitionsbank Berlin and the Freie Universitiit Berlin. 10 ISAAC Awards were presented to young researchers in analysis its applications and computation from all over the world on the basis of financial support from Siemens, Daimler Crysler, Motorola and the Berlin Mathematical Society and book gifts from Birkhauser Verlag, Elsevier, Kluwer Academic Publisher, Springer Verlag and World Scientific. The ISAAC is grateful to all these institutions, firms and publishers for their support. Due to the support from DFG and from Investitions bank Berlin many of the 362 registrated participants could be financially supported. Unfortunately the financial supports were granted too late to reach more people from former SU as the procedere for visa is still more than cumbersome and embassies are not at all flexible. Hence, a big part of the financial support could not be used and had to be returned. The 10 plenary lectures were 1. Antoniou, 1. Prigogine (Intern. Solvay Inst. Phys. Chem., Brussels): Irreversibility and the probabilistic description of unstable evolutions beyond the Hilbert space framework (read by 1. Antoniou), N.S. Bakhvalov, M.E. Eglit (Math. Mech. Dept., Lomonosov State Univ.

Inhalt

1. Decay and computability.- 2. Differential and pseudo-differential operators on graphs as models of mesoscopic systems.- 3. Homogenization of some multiparametric problems.- 4. Power geometry as a new calculus.- 5. A survey of Q-spaces and Q#-classes.- 6. Hyperbolically convex functions.- 7. Nevanlinna theory in characteristic P and applications.- 8. A new property of meromorphic functions and its applications.- 9. Complex zero decreasing sequences and the Riemann hypothesis II.- 10. Theory of reproducing kernels.- 11. Analytic functions and analytic functionals on some balls in the complex Euclidean space.- 12. Batteries and energy minimization problems.- 13. Vector-valued extentions of some classical theorems in harmonic analysis.- 14. Chaotic zone in the Bogdanov-Takens bifurcation for diffeomorphisms.- 15. Carleman estimates for a plate equation on a Riemann manifold with energy level terms.- 16. Hyperbolicity for systems.- 17. Strictly hyperbolic operators and approximate energies.- 18. Multiple highly oscillatory shock waves.- 19. Exponential time decay solutions of Schrödinger equations and of wave equations in even dimensional spaces.- 20. Inverse scattering for a small nonselfadjoint perturbation of the wave equation.