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1.
We investigate the relationship between the constants K(R) and K(T), where
is the exact constant in the Kolmogorov inequality, R is the real axis, T is a unit circle,
is the set of functions x L
p(G) such that x
(r) L
s(G), q, p, s [1, ], k, r N, k < r, We prove that if
thenK(R) = K(T),but if
thenK(R) K(T); moreover, the last inequality can be an equality as well as a strict inequality. As a corollary, we obtain new exact Kolmogorov-type inequalities on the real axis. 相似文献
2.
In this paper, we study the spaces B
pq
s
(G) and L
pq
s
(G) of functions f with positive exponent of smoothness s > 0 given on a domain
. The norms on these spaces are defined via integral norms of the difference of the function f of order m > s treated as a function of the point of the domain and of the difference increment. For an arbitrary domain
, we characterize these spaces in terms of the local approximations of the function by polynomials of degree m – 1. 相似文献
3.
IfK is a field of characteristic 0 then the following is shown. Iff, g, h: M
n
(K) K are non-constant solutions of the Binet—Pexider functional equation
相似文献
4.
Let p>q and let G be the group U(p, q) or Spin0(p, q). Let P=LN be the maximal parabolic subgroup of G with Levi subgroup
where
5.
Marc Levine 《K-Theory》1992,6(2):113-175
LetR be a commutative, semi-local ring,I
1, ...,I
s
ideals. In this paper, we define therelative Milnor K-groups of (R;I
1, ...,I
s
),K
p
M
(R;I
1, ...,I
s
), and show that these groups have many of the properties of the usual MilnorK-groups of a field. In particular, assuming a weak condition on the ideals, we show thatK
p
M
(R;I
1, ...,I
s
) is isomorphic to the weightp portion of the relative QuillenK-groupK
p
(R;I
1, ...,I
s
), after inverting (p–1)!. We also define the relative group homology of GL
n
(R;I
1, ...,I
s
), and show thatK
p
M
(R;I
1, ...,I
s
) is isomorphic toH
p
(GLp(R;I
1, ...,I
s
))/Im(H
p
(GL
p–1 (R;I
1, ...,I
s
))). Finally, we consider a generalization to the relative setting of Kato's conjecture asserting that the Galois symbol gives an isomorphism fromK
p
M
(F)/l
v
to
, and show that this relative version of Kato's conjecture implies the Quillen-Lichtenbaum conjectures asserting the Chern class:
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