Kim K, Krantz S G. Characterization of the Hilbert ball by its automorphism group[J]. Transactions of the American Mathematical Society, 2002, 354(7): 2797-2818.
7
Bedford E, Pinchuk S. CONVEX DOMAINS WITH NONCOMPACT AUTOMORPHISM GROUPS[J]. Sbornik Mathematics, 1995, 82(1): 1-20.
8
Eric Bedford · S I Pinchuk. Domains in Cn+1 with noncompact automorphism group. 1991.
9
Yau S. Perspectives on geometric analysis[C]., 2006, 10(1): 275-379.
10
Byun J, Cho H R. Explicit description for the automorphism group of the Kohn-Nirenberg domain[J]. Mathematische Zeitschrift, 2008, 263(2): 295-305.
Lenstra H W. Integer programming with a fixed number of variables[J]. Mathematics of Operations Research, 1983, 8(4): 538-548.
2
Niederreiter H. Quasi-Monte Carlo methods and pseudo-random numbers[J]. Bulletin of the American Mathematical Society, 1978, 84(6): 957-1041.
3
Victoria C P Chen · Kwokleung Tsui · Russell R Barton · Martin Meckesheimer. A review on design, modeling and applications of computer experiments. 2007.
4
Sprindzhuk V G. ACHIEVEMENTS AND PROBLEMS IN DIOPHANTINE APPROXIMATION THEORY[J]. Russian Mathematical Surveys, 1980, 35(4): 1-80.
5
Chen V C, Tsui K, Barton R R, et al. Ch. 7. A review of design and modeling in computer experiments[J]. Handbook of Statistics, 2003: 231-261.
6
Rickert J H. Simultaneous rational approximations and related diophantine equations.[J]. Mathematical Proceedings of the Cambridge Philosophical Society, 1993, 113(03): 461-472.
7
Niederreiter H. Methods for Estimating Discrepancy[C]., 1972: 203-236.
8
Dager R, Zuazua E. Controllability of star-shaped networks of strings[J]. Comptes Rendus De L Academie Des Sciences Serie I-mathematique, 2001, 332(7): 621-626.
9
Serge Lang. Transcendental numbers and diophantine approximations. 1971.
10
Mason R C. Norm form equations I[J]. Journal of Number Theory, 1986, 22(2): 190-207.
We establish sharp asymptotics for the$L$^{$p$}-norm of Hermite polynomials and prove convergence in distribution of suitably normalized Wick powers. The results are combined with numerical integration to study an extremal problem on Wiener chaos.