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1.
The purpose of the paper is to study the behavior at infinity of Fourier-Laplace transforms of distributions or more generally
plurisubharmonic functions u in Cn with bounds of the form
The set L∞(u) of limits of Ttu = u(t·)/t as t → +∞ is a compact T invariant subset of the set PH of plurisubharmonic functions in Cn with v(ξ) ≤H(Im ξ), ξ ∈ Cn, and equality on CRn. Here H is a supporting function associated with u, and T is chain recurrent on L∞(u). The behavior of functions in PH at CRn is studied in detail, which leads to conditions on a set M ⊂PH which guarantee that M = L∞(u) for some u as above. One can then choose u = log | F | where F is the Fourier-Laplace transform
of a distribution with compact support. 相似文献
2.
In this paper, we consider a multidimensional diffusion process with jumps whose jump term is driven by a compound Poisson
process. Let a(x,θ) be a drift coefficient, b(x,σ) be a diffusion coefficient respectively, and the jump term is driven by a Poisson random measure p. We assume that its intensity measure qθ has a finite total mass. The aim of this paper is estimating the parameter α = (θ,σ) from some discrete data. We can observe
n + 1 data at tin = ihn,
. We suppose hn → 0, nhn → ∞, nhn2 → 0.
Final version 20 December 2004 相似文献
3.
M. N. Sheremeta 《Mathematical Notes》1998,63(3):401-410
For the Dirichlet series corresponding to a functionF with positive exponents increasing to ∞ and with abscissa of absolute convergenceA ∈ (−∞, +∞], it is proved that the sequences (μ(σ, F
(m)
)) of maximal terms and (Λ(σ, F
(m)
)) of central exponents are nondecreasing to ∞ asm → ∞ for any givenσ <A, and
Necessary and sufficient conditions for putting the equality sign and replacing lim by lim in these relations are given.
Translated fromMatematicheskie Zametki, Vol. 63, No. 3, pp. 457–467, March, 1998. 相似文献
4.
Suppose that (F
n
)
n=1
∞
is a sequence of regular families of finite subsets of ℝ and (θ
n
)
n=1
∞
is a nonincreasing null sequence in (0,1). The mixed Tsirelson spaceT[(θ
n
,F
n
)
n=1
∞
] is the completion ofc
00 with respect to the implicitly defined norm
, where the last supremum is taken over all sequences (E
i
)
i=1
k
in [ℕ]<∞ such that maxE
i<minE
i
+1 and
. Necessary and sufficient conditions are obtained for the existence of higher order ℓ1-spreading models in every subspace generated by a subsequence of the unit vector basis ofT[(θ
n
,F
n
)
n=1
∞
]. 相似文献
5.
For x = (x 1, x 2, ..., x n ) ∈ ℝ+ n , the symmetric function ψ n (x, r) is defined by $\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } ,$\psi _n (x,r) = \psi _n \left( {x_1 ,x_2 , \cdots ,x_n ;r} \right) = \sum\limits_{1 \leqslant i_1 < i_2 \cdots < i_r \leqslant n} {\prod\limits_{j = 1}^r {\frac{{1 + x_{i_j } }}
{{x_{i_j } }}} } , 相似文献
6.
V. A. Kofanov 《Ukrainian Mathematical Journal》2009,61(6):908-922
For an arbitrary fixed segment [α, β] ⊂ R and given r ∈ N, A
r
, A
0, and p > 0, we solve the extremal problem
òab | x(k)(t) |qdt ? sup, q \geqslant p, k = 0, q \geqslant 1, 1 \leqslant k \leqslant r - 1, \int\limits_\alpha^\beta {{{\left| {{x^{(k)}}(t)} \right|}^q}dt \to \sup, \,\,\,\,q \geqslant p,\,\,\,k = 0,\,\,\,q \geqslant 1,\,\,\,\,1 \leqslant k \leqslant r - 1,} 相似文献
7.
D. R. Heath-Brown 《Proceedings Mathematical Sciences》1994,104(1):13-29
LetF(x) =F[x1,…,xn]∈ℤ[x1,…,xn] be a non-singular form of degree d≥2, and letN(F, X)=#{xεℤ
n
;F(x)=0, |x|⩽X}, where
. It was shown by Fujiwara [4] [Upper bounds for the number of lattice points on hypersurfaces,Number theory and combinatorics, Japan, 1984, (World Scientific Publishing Co., Singapore, 1985)] thatN(F, X)≪X
n−2+2/n
for any fixed formF. It is shown here that the exponent may be reduced ton - 2 + 2/(n + 1), forn ≥ 4, and ton - 3 + 15/(n + 5) forn ≥ 8 andd ≥ 3. It is conjectured that the exponentn - 2 + ε is admissable as soon asn ≥ 3. Thus the conjecture is established forn ≥ 10. The proof uses Deligne’s bounds for exponential sums and for the number of points on hypersurfaces over finite fields.
However a composite modulus is used so that one can apply the ‘q-analogue’ of van der Corput’s AB process.
Dedicated to the memory of Professor K G Ramanathan 相似文献
8.
Let f∈C
[−1,1]
″
(r≥1) and Rn(f,α,β,x) be the generalized Pál interpolation polynomials satisfying the conditions Rn(f,α,β,xk)=f(xk),Rn
′(f,α,β,xk)=f′(xk)(k=1,2,…,n), where {xk} are the roots of n-th Jacobi polynomial Pn(α,β,x),α,β>−1 and {x
k
″
} are the roots of (1−x2)Pn″(α,β,x). In this paper, we prove that
holds uniformly on [0,1].
In Memory of Professor M. T. Cheng
Supported by the Science Foundation of CSBTB and the Natural Science Foundatioin of Zhejiang. 相似文献
9.
For x = (x
1, x
2, …, x
n
) ∈ (0, 1 ]
n
and r ∈ { 1, 2, … , n}, a symmetric function F
n
(x, r) is defined by the relation
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