共查询到20条相似文献,搜索用时 687 毫秒
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V. N. Margaryan H. G. Ghazaryan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2017,52(5):211-220
A polynomial P(ξ) = P(ξ1,..., ξ n ) is said to be almost hypoelliptic if all its derivatives D ν P(ξ) can be estimated from above by P(ξ) (see [16]). By a theorem of Seidenberg-Tarski it follows that for each polynomial P(ξ) satisfying the condition P(ξ) > 0 for all ξ ∈ R n , there exist numbers σ > 0 and T ∈ R1 such that P(ξ) ≥ σ(1 + |ξ|) T for all ξ ∈ R n . The greatest of numbers T satisfying this condition, denoted by ST(P), is called Seidenberg-Tarski number of polynomial P. It is known that if, in addition, P ∈ I n , that is, |P(ξ)| → ∞ as |ξ| → ∞, then T = T(P) > 0. In this paper, for a class of almost hypoelliptic polynomials of n (≥ 2) variables we find a sufficient condition for ST(P) ≥ 1. Moreover, in the case n = 2, we prove that ST(P) ≥ 1 for any almost hypoelliptic polynomial P ∈ I2. 相似文献
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SanGuo Zhu 《中国科学 数学(英文版)》2016,59(2):337-350
We study the quantization for in-homogeneous self-similar measures μ supported on self-similar sets.Assuming the open set condition for the corresponding iterated function system, we prove the existence of the quantization dimension for μ of order r ∈(0, ∞) and determine its exact value ξ_r. Furthermore, we show that,the ξ_r-dimensional lower quantization coefficient for μ is always positive and the upper one can be infinite. A sufficient condition is given to ensure the finiteness of the upper quantization coefficient. 相似文献
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D. A. Korshunov 《Siberian Mathematical Journal》2009,50(4):663-666
We deduce an analog of the classical Wald’s identity ES τ = EτEξ in the case of the infinite mean of summands. We find the conditions on τ under which Emin(S τ , x) ~ EτE min(ξ, x) as x→∞. 相似文献
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Wolfgang Biegert 《Israel Journal of Mathematics》1966,4(2):97-112
Till now, we know Tauberian constants for the ‘Kreisverfahren’ with the conditions lim sup |n 1/2 a n|<∞ and lim sup |n 1 a n|<∞. Now, we obtain constants for the more general condition lim sup |n pan|<∞ with anyp(=∞<p<+∞). These constants are not always 0 or ∞, even if 1/2<p<1; therefore the Tauberian condition lim sup |n pan|<∞ is ‘appropriate’ for 1/2≦p≦1. 相似文献
6.
The main result of this paper asserts that the distribution density of any non-constant polynomial f(ξ1,ξ2,...) of degree d in independent standard Gaussian random variables ξ1 (possibly, in infinitely many variables) always belongs to the Nikol’skii–Besov space B1/d (R1) of fractional order 1/d (see the definition below) depending only on the degree of the polynomial. A natural analog of this assertion is obtained for the density of the joint distribution of k polynomials of degree d, also with a fractional order that is independent of the number of variables, but depends only on the degree d and the number of polynomials. We also give a new simple sufficient condition for a measure on Rk to possess a density in the Nikol’skii–Besov class Bα(R)k. This result is applied for obtaining an upper bound on the total variation distance between two probability measures on Rk via the Kantorovich distance between them and a certain Nikol’skii–Besov norm of their difference. Applications are given to estimates of distributions of polynomials in Gaussian random variables. 相似文献
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V. G. Karapetyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(5):285-296
A linear differential operator P(D) = P(D 1, …, D n ) with constant coefficients is called almost hypoelliptic if all the derivatives D α P of the characteristic polynomial P(ξ 1, …, ξ n ) can be estimated by P. The paper proves that if P is an almost hypoelliptic operator and f is an infinitely differentiable function, square-summable with a definite exponential weight, then any square summable with the same weight solution u of the equation P(D)u = f is again an infinitely differentiable function and P(ξ) → ∞ as ξ → ∞. 相似文献
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Let L be a lattice of finite length, ξ = (x 1,…, x k )∈L k , and y ∈ L. The remoteness r(y, ξ) of y from ξ is d(y, x 1)+?+d(y, x k ), where d stands for the minimum path length distance in the covering graph of L. Assume, in addition, that L is a graded planar lattice. We prove that whenever r(y, ξ) ≤ r(z, ξ) for all z ∈ L, then y ≤ x 1∨?∨x k . In other words, L satisfies the so-called c 1 -median property. 相似文献
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Vladimir Piterbarg Goran Popivoda Siniša Stamatović 《Lithuanian Mathematical Journal》2017,57(1):128-141
Let ξ(t), t ∈ [0, T],T > 0, be a Gaussian stationary process with expectation 0 and variance 1, and let η(t) and μ(t) be other sufficiently smooth random processes independent of ξ(t). In this paper, we obtain an asymptotic exact result for P(sup t∈[0,T](η(t)ξ(t) + μ(t)) > u) as u→∞. 相似文献
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We study the sharp Nikol’skii inequality between the uniform norm and the L q norm of algebraic polynomials of a given (total) degree n ≥ 1 on the unit sphere \(\mathbb{S}^{m - 1} \) of the Euclidean space ? m for 1 ≤ q < ∞. We prove that the polynomial ? n in one variable with unit leading coefficient that deviates least from zero in the space L q ψ (?1, 1) of functions f such that |f| q is summable over (?1, 1) with the Jacobi weight ψ(t) = (1 - t)α(1 + t)β, α = (m - 1)/2, β = (m - 3)/2 as a zonal polynomial in one variable t = ξ m , where x = (ξ 1, ξ 2, …, ξ m ) ∈ \(\mathbb{S}^{m - 1} \), is (in a certain sense, unique) extremal polynomial in the Nikol’skii inequality on the sphere \(\mathbb{S}^{m - 1} \). The corresponding one-dimensional inequalities for algebraic polynomials on a closed interval are discussed. 相似文献
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Ken-Ichi Yoshikawa 《Mathematische Annalen》2007,337(1):61-89
Let π: X → S be a holomorphic map from a compact Kähler manifold (X,g X ) to a compact Riemann surface S. Let Σπ be the critical locus of π and let Δ = π(Σπ) be the discriminant locus. Let (ξ, h ξ) be a holomorphic Hermitian vector bundle on X. We determine the singularity of the Quillen metric on det Rπ*ξ near Δ with respect to g X | TX/S and h ξ. 相似文献
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Let (M, g) be a compact smooth connected Riemannian manifold (without boundary) of dimension N ≥ 7. Assume M is symmetric with respect to a point ξ 0 with non-vanishing Weyl’s tensor. We consider the linear perturbation of the Yamabe problem We prove that for any k ∈ ?, there exists ε k > 0 such that for all ε ∈ (0, ε k ) the problem (P ?? ) has a symmetric solution u ε , which looks like the superposition of k positive bubbles centered at the point ξ 0 as ε → 0. In particular, ξ 0 is a towering blow-up point.
相似文献
$$ (P_{\epsilon })\qquad -\mathcal {L}_{g} u+\epsilon u=u^{\frac {N+2}{N-2}}\ \text { in }\ (M,g) . $$
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D. A. Korshunov 《Siberian Mathematical Journal》2005,46(6):1077-1081
We study the asymptotic tail behavior of the maximum M = max{0,S n ,n ≥ = 1} of partial sums S n = ξ1 + ? + ξ n of independent identically distributed random variables ξ1,ξ2,... with negative mean. We consider the so-called Cramer case when there exists a β > 0 such that E e βξ1 = 1. The celebrated Cramer-Lundberg approximation states the exponential decay of the large deviation probabilities of M provided that Eξ1 e βξ1 is finite. In the present article we basically study the critical case Eξ1 e βξ1 = ∞. 相似文献
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Francisco Javier González Vieli 《Czechoslovak Mathematical Journal》2017,67(4):1059-1070
Given a distribution T on the sphere we define, in analogy to the work of ?ojasiewicz, the value of T at a point ξ of the sphere and we show that if T has the value τ at ξ, then the Fourier-Laplace series of T at ξ is Abel-summable to τ. 相似文献
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A. G. Kamalyan V. V. Simonyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2008,43(4):233-245
The paper suggests an approach to one-dimensional pseudodifferential equations of nonnegative order, whose symbols are of the form A 1(ξ) + th(kx + ω)A 2(ξ). The method is based on reduction of the considered pseudodifferential equation to an integral equation. Some integral representations of solutions are found. 相似文献
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Vladimir I. Piterbarg 《Extremes》2016,19(2):253-272
Let ξ ( t)=(ξ 1(t),…,ξ d (t)) be a Gaussian stationary vector process. Let \(g:{\mathbb {R}}^{d}\rightarrow {\mathbb {R}}\) be a homogeneous function. We study probabilities of large extrema of the Gaussian chaos process g(ξ(t)). Important examples include \(g(\mathbf {\boldsymbol {\xi }}(t))={\prod }_{i=1}^{d}\xi _{i}(t)\) and \(g(\mathbf {\boldsymbol {\xi }}(t))={\sum }_{i=1}^{d}a_{i}{\xi _{i}^{2}}(t)\). We review existing results partially obtained in collaboration with E. Hashorva, D. Korshunov, and A. Zhdanov. We also present the principal methods of our investigations which are the Laplace asymptotic method and other asymptotic methods for probabilities of high excursions of Gaussian vector process’ trajectories. 相似文献
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M. M. Malamud H. Neidhardt V. V. Peller 《Functional Analysis and Its Applications》2017,51(3):185-203
In this paper we prove that for an arbitrary pair {T 1, T 0} of contractions on Hilbert space with trace class difference, there exists a function ξ in L 1(T) (called a spectral shift function for the pair {T 1, T 0}) such that the trace formula trace(f(T 1) ? f(T 0)) = ∫T f′(ζ)ξ(ζ)dζ holds for an arbitrary operator Lipschitz function f analytic in the unit disk. 相似文献
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In 1985, Bloom characterized the boundedness of the commutator [b, H] as a map between a pair of weighted Lp spaces, where both weights are in Ap. The characterization is in terms of a novel BMO condition. We give a ‘modern’ proof of this result, in the case of p = 2. In a subsequent paper, this argument will be used to generalize Bloom’s result to all Calderón–Zygmund operators and dimensions. 相似文献
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Let ξ(t) be a zero-mean stationary Gaussian process with the covariance function r(t) of Pickands type, i.e., r(t) = 1 ? |t| α + o(|t| α ), t → 0, 0 < α ≤ 2, and η(t), ζ(t) be periodic random processes. The exact asymptotic behavior of the probabilities P(max t∈[0,T] η(t)ξ(t) > u), P(max t∈[0,T] (ξ(t) + η(t)) > u) and P(max t∈[0,T] (η(t)ξ(t) + ζ(t)) > u) is obtained for u → ∞ for any T > 0 and independent ξ(t), η(t), ζ(t). 相似文献
20.
William A. Veech 《Journal d'Analyse Mathématique》2018,135(2):413-436
Let S be the set of square-free natural numbers. A Hilbert-Schmidt operator, A, associated to the Möbius function has the property that it maps from \({ \cup _{0 < r < \infty }}{l^r}(s)\) to \({ \cap _{0 < r < \infty }}{l^r}(s)\), injectively. If 0 < r< 2 and ξ ∈ lr (S), the series \({f_\zeta } = \sum\nolimits_{n \in s} {A\zeta (x)cos2\pi nx} \) converges uniformly to an element of fξR0, i.e., a periodic, even, continuous function with equally spaced Riemann sums, \(\sum\nolimits_{j = 0}^{N - 1} {{f_\zeta }} (j/N) = 0,N = 1,2....\) If \({A_{\zeta \lambda }} = \lambda {\zeta _\lambda },{\zeta _\lambda }(1) = 1\), then ξλ is multiplicative. If \({f_{{\zeta _\lambda }}} \in {\Lambda _a}\), the space of α-Lipschitz continous functions, for some α > 0, and if χ is any Dirichlet character, then L(s, χ) ≠ 0, Res > 1 ? α. Conjecturally, the Generalized Riemann Hypothesis (GRH) is equivalent to fξ ∈ Λα, α < 1/2, ξ ∈ lr (S), 0 < r < 2. Using a 1991 estimate by R. C. Baker and G. Harman, one finds GRH implies fξ ∈ Λα, α < 1/4, ξ ∈ lr (S), 0 < r < 2. The question of whether R0 ∩ Λα ≠ {0} for some positive α > 0 is open. 相似文献