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1.
Point sets {A1,...,An} in
, d 2, are considered that have barycenter at the origin and, for a certain collection of even exponents 2,4,...,2p, possess power invariants Ik in the following sense. Let Sd-1(R) be the sphere with center at the origin and radius R and let M Sd-1(R). Then the
, do not depend on the position of M on Sd-1(R). Bibliography: 14 titles. 相似文献
2.
Michel Talagrand 《Journal of Theoretical Probability》1992,5(2):327-331
Consider a (complex) Banach spaceX, such thatX CO, and vectors(X
i
)
i
ofX. Consider an independent standard normal sequence(g
i
)
i
. Then if anX-valued random Fourier series |k|
n
e
ikt
g
k
x
k
satisfies
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3.
We compute the joint entropy ofd commuting automorphisms of a compact metrizable group. LetR
d
= [u
1
±1
,...,[d
1
±1
] be the ring of Laurent polynomials ind commuting variables, andM be anR
d
-module. Then the dual groupX
M
ofM is compact, and multiplication onM by each of thed variables corresponds to an action
M
of
d
by automorphisms ofX
M
. Every action of
d
by automorphisms of a compact abelian group arises this way. IffR
d
, our main formula shows that the topological entropy of
is given by
|