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1.
We establish conditions under which, in three-dimensional relaxation systems of the form {fx066-01}, where 0 < ε << 1, |μ|
<< 1, and ƒ, g ∈ C
∞, the so-called “blue-sky catastrophe” is observed, i.e., there appears a stable relaxation cycle whose period and length
tend to infinity as μ tends to a certain critical value μ*(ε), μ*(0) 0 = 0.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 63–72, January, 2008. 相似文献
2.
M. Ratner 《Israel Journal of Mathematics》1974,17(4):380-391
We consider a special flowS
t over a shift in the space of sequences (X, μ) constructed using a continuousf with {fx380-1}
We formulate a condition for μ such that theK-flowS
t is aB-flow.
A note on the paperGeodesic flows are Bernoullian by D. Ornstein and B. Weiss. 相似文献
3.
H. H. Schaefer 《Israel Journal of Mathematics》1984,48(2-3):196-204
Let (X, Σ, μ) be a σ-finite measure space,T a compact irreducible (positive, linear) operator onL
p (μ) (1≦p<+∞). It is shown that the spectral radiusr ofT is characterized by the minimax property {fx196-1} where ∑0 denotes the ring of sets of finite measure and whereQ denotes the set of all, almost everywhere positive functions inL
p. Moreover, ifr>0 then equality on either side is assumed ifff is the (essentially unique) positive eigenfunction ofT. Various refinements are given in terms of corresponding relations for irreducible finite rank operators approximatingT.
Dedicated to H. G. Tillmann on his 60th birthday 相似文献
4.
If 0 < p < ∞ and α > − 1, the space
consists of those functions f which are analytic in the unit disc
and have the property that f ′ belongs to the weighted Bergman space Aαp. In 1999, Z. Wu obtained a characterization of the Carleson measures for the spaces
for certain values of p and α. In particular, he proved that, for 0 < p ≤ 2, the Carleson measures for the space
are precisely the classical Carleson measures. Wu also conjectured that this result remains true for 2 < p < ∞. In this paper we prove that this conjecture is false. Indeed, we prove that if 2 < p < ∞, then there exists g analytic in
such that the measure μg,p on
defined by dμg,p (z) = (1 − |z|2)p - 1| g ′ (z)|p dx dy is not a Carleson measure for
but is a classical Carleson measure. We obtain also some sufficient conditions for multipliers of the spaces
相似文献
5.
The inverse problem of reconstructing the coefficients A and B in the equation {fx379-01} in the half-plane z > 0 is considered.
It is assumed that an instantaneous point source at z = 0 generates a wave field U(t, z, x), which is known on the boundary.
It is also known that the coefficients A and B can be represented in the form {fx379-02}. Here ε is a small parameter. An
algorithm for determinating the coefficients A0, B0, A1, and B1 with accuracy O(ε2) is constructed. Bibliography: 5 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 354, 2008, pp. 81–99. 相似文献
6.
Denote by γ the Gauss measure on ℝ
n
and by ${\mathcal{L}}${\mathcal{L}} the Ornstein–Uhlenbeck operator. In this paper we introduce a Hardy space
\mathfrakh1g{{\mathfrak{h}}^1}{{\rm \gamma}} of Goldberg type and show that for each u in ℝ ∖ {0} and r > 0 the operator (rI+L)iu(r{\mathcal{I}}+{\mathcal{L}})^{iu} is unbounded from
\mathfrakh1g{{\mathfrak{h}}^1}{{\rm \gamma}} to L
1γ. This result is in sharp contrast both with the fact that (rI+L)iu(r{\mathcal{I}}+{\mathcal{L}})^{iu} is bounded from H
1γ to L
1γ, where H
1γ denotes the Hardy type space introduced in Mauceri and Meda (J Funct Anal 252:278–313, 2007), and with the fact that in the Euclidean case (rI-D)iu(r{\mathcal{I}}-\Delta)^{iu} is bounded from the Goldberg space
\mathfrakh1\mathbbRn{{\mathfrak{h}}^1}{{\mathbb{R}}^n} to L
1ℝ
n
. We consider also the case of Riemannian manifolds M with Riemannian measure μ. We prove that, under certain geometric assumptions on M, an operator T{\mathcal{T}}, bounded on L
2
μ, and with a kernel satisfying certain analytic assumptions, is bounded from H
1
μ to L
1
μ if and only if it is bounded from
\mathfrakh1m{{\mathfrak{h}}^1}{\mu} to L
1
μ. Here H
1
μ denotes the Hardy space introduced in Carbonaro et al. (Ann Sc Norm Super Pisa, 2009), and
\mathfrakh1m{{\mathfrak{h}}^1}{\mu} is defined in Section 4, and is equivalent to a space recently introduced by M. Taylor (J Geom Anal 19(1):137–190, 2009). The case of translation invariant operators on homogeneous trees is also considered. 相似文献
7.
Piotr Niemiec 《Rendiconti del Circolo Matematico di Palermo》2008,57(3):391-399
The aim of the paper is to prove that every f ∈ L
1([0,1]) is of the form f = , where j
n,k
is the characteristic function of the interval [k- 1 / 2
n
, k / 2
n
) and Σ
n=0∞Σ
k=12n
|a
n,k
| is arbitrarily close to ||f|| (Theorem 2). It is also shown that if μ is any probabilistic Borel measure on [0,1], then for any ɛ > 0 there exists a sequence (b
n,k
)
n≧0
k=1,...,2n
of real numbers such that and for each Lipschitz function g: [0,1] → ℝ (Theorem 3).
相似文献
8.
Feynman-Kac semigroup with discontinuous additive functionals 总被引:1,自引:0,他引:1
Renming Song 《Journal of Theoretical Probability》1995,8(4):727-762
LetX be a symmetric stable process of index α, 0<α<2, inRd, let μ be a (signed) Radon measure onRd belonging to the Kato classKd, α and letF be a Borel function onRd×Rd satisfying certain conditions. Suppose thatA
t
μ
is the continuous additive functional with μ as its Revuz measure and
相似文献
9.
V. G. Krotov 《Ukrainian Mathematical Journal》2010,62(3):441-451
We prove the following statement, which is a quantitative form of the Luzin theorem on C-property: Let (X, d, μ) be a bounded metric space with metric d and regular Borel measure μ that are related to one another by the doubling condition. Then, for any function f measurable on X, there exist a positive increasing function η ∈ Ω (η(+0) = 0 and η(t)t
−a
decreases for a certain a > 0), a nonnegative function g measurable on X, and a set E ⊂ X, μE = 0 , for which
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