Unsolved nonstandard problems. (English) Zbl 1027.46093

Kusraev, A. G.; Kutateladze, S. S.

Vladikavkaz. Mat. Zh. 2, No. 2, 26-45 (2000).

Summary: A list of unsolved problems is given which stem from various branches of analysis and seemingly deserve attention of the novices of nonstandard analysis. The list consists of 88 problems and contains not only simple questions for training but also topics for serious research intended mostly at the graduate and post graduate level. The problems are arranged in the following sections: (1) Nonstandard hulls and Loeb measures. (2) Hyperfinite approximation and spectral theory. (3) Combining nonstandard methods. (4) Convex analysis and extremal problems. (5) Miscellany. The list of references contains 83 items.

MSC:

46S20	Nonstandard functional analysis
03H05	Nonstandard models in mathematics
00A07	Problem books
47S20	Nonstandard operator theory
46-02	Research exposition (monographs, survey articles) pertaining to functional analysis

Keywords:

nonstandard hull; Loeb measure; hyperfinite approximation; spectral theory