ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

11. Mathematical Physics

1991 MS Classification: 28, 32, 35, 46, 81 Petersson, Henrik, Växjö University, Sweden Properties of analytical maps on infinite dimensional locally convex spaces A space of analytical functions, denoted by A(X), defined on a finite dimensional locally convex space X is studied. A(X) consists of all functions that ate continuous on compact sets and whose restrictions to any finite dimensional plane x + N, where N ⊂ X is a finite dimensional subspace and x ∈ X, is a holomorfic functionl. A(X) is given the topology of uniform convergence on compact sets. An continuously embedded subspace A_{c}(X) ⊂ A(X) (Cylindrical analytical functions), is also considerd. In particular, the Fourier transforms of the dual spaces A′(X) and A′_{c}(X) is studied and the Paley-Wiener theorems are generalised. Some of these results will be presented. The results can be used in the Quantum field theory in the study of the Feynman integral. Reference: A. YU. Khrennikov, Infinite-dimensional pseudodifferential operators, Math. USSR Izvestiya Vol. 31(1998), No. 3.