ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 42,33 Ash, J. Marshall and Wang, Gang, DePaul University, USA Nonuniqueness for smooth uniformly bounded orthonormal systems An orthonormal on the interval [0, 1] system of functions φ_{n}(x) will be said to have the nonuniqueness property if there are constants c_{n}, not all zero, such that ∑ c_{n}φ_{n} (x) = 0 for every x ∈ [0, 1] . A uniformly bounded orthonormal system of continuous functions with the nonuniqueness property was discovered by G. M. Mu\v segian and R. I. Ovsepjan. {The uniqueness of orthogonal series. (Russian) Izv. Akad. Nauk Armjan. SSR Ser. Mat. 4(1969), 259–266. MR 42 #3485} We will present here a uniformly bounded orthonormal system of smoother functions with the nonuniqueness property.