ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 46F15 46F20 32C35 Pilipović, Stevan, University of Novi Sad, Yugoslavia Suppleness of Some Quotient Spaces of Microfunctions We develop the theory of some quotient spaces of microfunctions and state the suppleness of the sheaves of these functions which is important for the theory of microdifferential equations. Our investigations enable us to introduce the notions SS^{∗} and SS_{∗} for hyperfunctions. Our basic result is the following theorem:

a) The quotient sheaf Db_{M}^{∗}/Df_{M}^{∗} is supple.

b) The sheaves C_{M}^{1∗} and C_{M}^{1/∗} are flabby and the following sequences are exact

0 → Df_{M}^{∗} → B_{M} → π_{∗}C_{M}^{1,∗} → 0,
0 → Db_{M}^{∗} → B_{M} → π_{∗}C_{M}^{1/∗} → 0.

c) Let 1 ≤ † ≤ ∗. The sheaves C_{M}^{†,∗} and C_{M}^{†/∗} are supple and the sequences

0 → Df_{M}^{∗} → D_{M}^{†} → π_{∗}C_{M}^{†,∗} → 0,
0 → Db_{M}^{∗} → Db_{M}^{†} → π_{∗}C_{M}^{†/∗} → 0,

are exact.

d) Let 1 ≤ ∗ ≤ †. The sheaf C_{M}^{d,†,∗} is supple and the sequence

0 → Df_{M}^{∗} → Df_{M}^{†} → π_{∗}C_{M}^{d,†,∗} → 0

is exact.