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1.
V. P. Sklyarov 《Computational Mathematics and Mathematical Physics》2011,51(10):1679-1684
The behavior of the graph of the function Z
n
(t) = ∥Z
n
′(·, t)∥/∥Z
n
(·, t)∥ is discussed in the case where the functions Z
n
(x, t) are the Zolotarev polynomials and the norm is a weighted sup norm. Based on calculations performed for various weights,
it is conjectured that the characteristic jump in Z
n
(t) in the case of the Laguerre weight on a semiaxis is caused by the fact that the weight function is not symmetric about the
midpoint of the interval. 相似文献
2.
F. M. Mukhamedov 《Mathematical Notes》2000,67(1):81-86
In this paper an analog of the Blum-Hanson theorem for quantum quadratic processes on the von Neumann algebra is proved, i.e.,
it is established that the following conditions are equivalent:
Translated fromMatematicheskie Zametki, Vol. 67, No. 1, pp. 102–109, January, 2000. 相似文献
i) | P( t )x is weakly convergent tox 0; |
ii) | for any sequence {a n} of nonnegative integrable functions on [1, ∞) such that ∝ 1 ∞ a n(t)dt=1 for anyn and lim n→∞ ∥a n∥∞=0, the integral ∝ 1 ∞ a n(t)P( t )x dt is strongly convergent tox 0 inL 2(M, ϕ), wherex ɛM,P( t ) is a quantum quadratic process,M is a von Neumann algebra, andϕ is an exact normal state onM. |
3.
Let K be a complete ultrametric algebraically closed field and let A be the K-Banach algebra of bounded analytic functions in the disk D: |x| < 1. Let Mult(A, ∥ · ∥) be the set of continuous multiplicative semi-norms of A, let Mult
m
(A, ∥ · ∥) be the subset of the ϕ ∈ Mult(A, ∥ · ∥) whose kernel is a maximal ideal and let Mult
a
(A, ∥ · ∥) be the subset of the ϕ ∈ Mult
m
(A, ∥ · ∥) whose kernel is of the form (x − a)A, a ∈ D ( if ϕ ∈ Mult
m
(A, ∥ · ∥) \ Mult
a
(A, ∥ · ∥), the kernel of ϕ is then of infinite codimension). We examine whether Mult
a
(A, ∥ · ∥) is dense inside Mult
m
(A, ∥ · ∥) with respect to the topology of simple convergence. This a first step to the conjecture of density of Mult
a
(A, ∥ · ∥) in the whole set Mult(A, ∥ · ∥): this is the corresponding problem to the well-known complex corona problem. We notice that if ϕ ∈ Mult
m
(A, ∥ · ∥) is defined by an ultrafilter on D, then ϕ lies in the closure of Mult
a
(A, ∥ · ∥). Particularly, we show that this is case when a maximal ideal is the kernel of a unique ϕ ∈ Multm(A, ∥ · ∥). Particularly, when K is strongly valued all maximal ideals enjoy this property. And we can prove this is also true when K is spherically complete, thanks to the ultrametric holomorphic functional calculus. More generally, we show that if ψ ∈ Mult(A, ∥ · ∥) does not define the Gauss norm on polynomials (∥ · ∥), then it is defined by a circular filter, like on rational
functions and analytic elements. As a consequence, if ψ ∈
Multm(A, ∥ · ∥) \ Multa(A, ∥ · ∥) or if φ does not lie in the closure of Mult
a
(A, ∥ · ∥), then its restriction to polynomials is the Gauss norm. The first situation does happen. The second is unlikely.
The text was submitted by the authors in English. 相似文献
4.
In this paper, we study the L
p
(2 ⩽ p ⩽ +∞) convergence rates of the solutions to the Cauchy problem of the so-called p-system with nonlinear damping. Precisely, we show that the corresponding Cauchy problem admits a unique global solution (v(x,t), u(x,t)) and such a solution tends time-asymptotically to the corresponding nonlinear diffusion wave (ῡ(x,t), ū(x,t)) governed by the classical Darcys’s law provided that the corresponding prescribed initial error function (w
0(x), z
0(x)) lies in (H
3 × H
2) (ℝ) and |v
+ − v
−| + ∥w
0∥3 + ∥z
0∥2 is sufficiently small. Furthermore, the L
p
(2 ⩽ p ⩽ +∞) convergence rates of the solutions are also obtained. 相似文献
5.
Incompleteness and minimality of complex exponential system 总被引:3,自引:0,他引:3
Guan-tie DENG School of Mathematical Sciences Beijing Normal University Beijing China 《中国科学A辑(英文版)》2007,50(10):1467-1476
A necessary and sufficient condition is obtained for the incompleteness of a complex exponential system E(A,M)in C_α,where C_αis the weighted Banach space consisting of all complex continuous functions f on the real axis R with f(t)exp(-α(t))vanishing at infinity,in the uniform norm‖f‖_α=sup{|f(t)e~(-α(t))|:t∈R}with respect to the weightα(t).If the incompleteness holds, then the complex exponential system E(?)is minimal and each function in the closure of the linear span of complex exponential system E(?)can be extended to an entire function represented by a Taylor-Dirichlet series. 相似文献
6.
Let L
p
(S), 0 < p < +∞, be a Lebesgue space of measurable functions on S with ordinary quasinorm ∥·∥
p
. For a system of sets {B
t
|t ∈ [0, +∞)
n
} and a given function ψ: [0, +∞)
n
↦ [ 0, +∞), we establish necessary and sufficient conditions for the existence of a function f ∈ L
p
(S) such that inf {∥f − g∥
p
p
g ∈ L
p
(S), g = 0 almost everywhere on S\B
t
} = ψ (t), t ∈ [0, +∞)
n
. As a consequence, we obtain a generalization and improvement of the Dzhrbashyan theorem on the inverse problem of approximation
by functions of the exponential type in L
2.
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 8, pp. 1116–1127, August, 2006. 相似文献
7.
Tao Xiangxing 《分析论及其应用》1996,12(2):13-19
Let μ be a measure on the upper half-space R
+
n+1
, and v a weight onR
n, we give a characterization for the pair (v, μ) such that ∥M(fv)∥L
Θ
(μ) ⩽ c ∥f∥L
Θ
(μ), where Φ is an N-function satisfying Δ2 condition andMf(x,t), is the maximal function onR
+
n+1
, which was introduced by Ruiz, F. and Torrea, J..
Supported by NSFC. 相似文献
8.
We consider the fast diffusion equation (FDE) u
t
= Δu
m
(0 < m < 1) on a nonparabolic Riemannian manifold M. Existence of weak solutions holds. Then we show that the validity of Euclidean–type Sobolev inequalities implies that certain
L
p
−L
q
smoothing effects of the type ∥u(t)∥
q
≤ Ct
−α ∥u
0∥γ
p
, the case q = ∞ being included. The converse holds if m is sufficiently close to one. We then consider the case in which the manifold has the addition gap property min σ(−Δ) > 0. In that case solutions vanish in finite time, and we estimate from below and from above the extinction time.
相似文献
9.
A semigroup [T(t)] on a Hilbert space is exponentially stable if there exist real constants M≥1 and α>0 such that ∥T(t)∥≤Me
−αt
for every t≥0. If [T(t)] is a strongly continuous contraction semigroup, then it is proved that we can set M=1 in the definition of exponential stability if and only if the generator A of [T(t)] is boundedly strict dissipative (just a strict dissipative A is not enough). 相似文献
10.
Von Neumann-Jordan Constants of Absolute Normalized Norms on C^n 总被引:1,自引:0,他引:1
In this note, we give some estimations of the Von Neumann-Jordan constant C
N J
(∥·∥ψ) of Banach space (ℂ
n
, ∥·∥ψ), where ∥·∥ψ is the absolute normalized norm on ℂ
n
given by function ψ. In the case where ψ and φ are comparable, n=2 and C
N J
(∥·∥ψ)=1, we obtain a formula of computing C
N J
(∥·∥ψ). Our results generalize some results due to Saito and others.
Received May 11, 2002, Accepted November 20, 2002
This work is partly supported by NNSF of China (No. 19771056) 相似文献
11.
Let L be the infinitesimal generator of an analytic semigroup on L2 (Rn) with suitable upper bounds on its heat kernels. Assume that L has a bounded holomorphic functional calculus on L2(Rn). In this paper,we define the Littlewood- Paley g function associated with L on Rn × Rn, denoted by GL(f)(x1, x2), and decomposition, we prove that ‖SL(f)‖p ≈‖GL(f)‖p ≈‖f‖p for 1 < p <∞. 相似文献
12.
ON THE DIFFUSION PHENOMENON OF QUASILINEAR HYPERBOLICWAVES 总被引:1,自引:0,他引:1
YANG Han 《数学年刊B辑(英文版)》2000,21(1):63-70
Introduction1.1.ConsiderthefollowingquasilinearhyperbolicCauchyproblemwithlineardamping{:;;!OTt=-:i<:,;>>L06,(11)wherexER",t20,anda(.)isasmoothfunctionsatisfyinga(y)~1 O(lyl")aslyl-0,orEN.(1.2)Thepurposeofthispaperistoshowthat,atleastwhenn53,theasymptoticprofileofthesolutionu(x,t)of(l.1)isgivenbythesolutionv(x,t)ofthecorrespondingparabolicproblem{:;.t>ivj:相似文献
13.
D. V. Gusak 《Ukrainian Mathematical Journal》2000,52(2):234-248
For a process ξ(t = ξ1(t)+χ(t), t≥0, ξ(0) = 0, inhomogeneous with respect to time, we investigate the ruin problem associated with the corresponding random
walk in a finite interval, (here, ξ1 (t) is a homogeneous Poisson process with positive integer-valued jumps and χ(t) is an inhomogeneous lower-semicontinuous process with integer-valued jumps ξ
n
≥-1). 相似文献
14.
Fu Qing GAO 《数学学报(英文版)》2007,23(8):1527-1536
Let {Xn;n≥ 1} be a sequence of independent non-negative random variables with common distribution function F having extended regularly varying tail and finite mean μ = E(X1) and let {N(t); t ≥0} be a random process taking non-negative integer values with finite mean λ(t) = E(N(t)) and independent of {Xn; n ≥1}. In this paper, asymptotic expressions of P((X1 +… +XN(t)) -λ(t)μ 〉 x) uniformly for x ∈[γb(t), ∞) are obtained, where γ〉 0 and b(t) can be taken to be a positive function with limt→∞ b(t)/λ(t) = 0. 相似文献
15.
Let (X
t
, Y
t
) be a pure jump Markov process: the state X
t
takes real values and the observation Y
t
is a counting process. The two processes are allowed to have common jump times. Let ϕ(X(⋅)) be a functional of the state trajectory restricted to the time interval [0, T] . If we change the infinitesimal parameters and/ or the initial distribution, then we introduce an error in computing the conditional law of ϕ(X(⋅)) given the observation up to time T . In this paper we give an explicit L
1
-bound for this error.
Accepted 9 March 2001. Online publication 20 June 2001. 相似文献
16.
Tomasz Komorowski 《Probability Theory and Related Fields》2001,121(4):525-550
We consider the asymptotic behavior of the solutions ofscaled convection-diffusion equations ∂
t
u
ɛ
(t, x) = κΔ
x
(t, x) + 1/ɛV(t/ɛ2,xɛ) ·∇
x
u
ɛ
(t, x) with the initial condition u
ɛ(0,x) = u
0(x) as the parameter ɛ↓ 0. Under the assumptions that κ > 0 and V(t, x), (t, x) ∈R
d
is a d-dimensional,stationary, zero mean, incompressible, Gaussian random field, Markovian and mixing in t we show that the laws of u
ɛ(t,·), t≥ 0 in an appropriate functional space converge weakly, as ɛ↓ 0, to a δ-type measureconcentrated on a solution of a certain
constant coefficient heat equation.
Received: 23 March 2000 / Revised version: 5 March 2001 / Published online: 9 October 2001 相似文献
17.
Consider the Cauchy problem ∂u(x, t)/∂t = ℋu(x, t) (x∈ℤd, t≥ 0) with initial condition u(x, 0) ≡ 1 and with ℋ the Anderson Hamiltonian ℋ = κΔ + ξ. Here Δ is the discrete Laplacian, κ∈ (0, ∞) is a diffusion constant,
and ξ = {ξ(x): x∈ℤ
d
} is an i.i.d.random field taking values in ℝ. G?rtner and Molchanov (1990) have shown that if the law of ξ(0) is nondegenerate,
then the solution u is asymptotically intermittent.
In the present paper we study the structure of the intermittent peaks for the special case where the law of ξ(0) is (in the
vicinity of) the double exponential Prob(ξ(0) > s) = exp[−e
s
/θ] (s∈ℝ). Here θ∈ (0, ∞) is a parameter that can be thought of as measuring the degree of disorder in the ξ-field. Our main result
is that, for fixed x, y∈ℤ
d
and t→∈, the correlation coefficient of u(x, t) and u(y, t) converges to ∥w
ρ∥−2
ℓ2Σz ∈ℤd
w
ρ(x+z)w
ρ(y+z). In this expression, ρ = θ/κ while w
ρ:ℤd→ℝ+ is given by w
ρ = (v
ρ)⊗
d
with v
ρ: ℤ→ℝ+ the unique centered ground state (i.e., the solution in ℓ2(ℤ) with minimal l
2-norm) of the 1-dimensional nonlinear equation Δv + 2ρv log v = 0. The uniqueness of the ground state is actually proved only for large ρ, but is conjectured to hold for any ρ∈ (0, ∞).
empty
It turns out that if the right tail of the law of ξ(0) is thicker (or thinner) than the double exponential, then the correlation
coefficient of u(x, t) and u(y, t) converges to δ
x, y
(resp.the constant function 1). Thus, the double exponential family is the critical class exhibiting a nondegenerate correlation
structure.
Received: 5 March 1997 / Revised version: 21 September 1998 相似文献
18.
Yu. B. Koval' 《Ukrainian Mathematical Journal》1994,46(6):832-836
We prove that integral functionals, whose integrands are bounded functions of a Wiener process on a cylinder, weakly converge
to the processw
1(τ(t)), τ(t) = β1
t + (β2 − β1)mes {s:w
2(s)≥0,s<t}, wherew
1(t andw
2(t) are independent one-dimensional Wiener processes, β1 and β2 are nonrandom values, and β2≥β1≥0.
Kiev University, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 6, pp. 765–768, June, 1994. 相似文献
19.
Cyril Houdayer 《Mathematische Annalen》2010,346(4):969-989
We give examples of non-amenable infinite conjugacy classes groups Γ with the Haagerup property, weakly amenable with constant
Λcb(Γ) = 1, for which we show that the associated II1 factors L(Γ) are strongly solid, i.e. the normalizer of any diffuse amenable subalgebra P ì L(G){P \subset L(\Gamma)} generates an amenable von Neumann algebra. Nevertheless, for these examples of groups Γ, L(Γ) is not isomorphic to any interpolated free group factor L(F
t
), for 1 < t ≤ ∞. 相似文献
20.
Gerald Kuba 《Mathematica Slovaca》2009,59(3):349-356
Let ℛ
n
(t) denote the set of all reducible polynomials p(X) over ℤ with degree n ≥ 2 and height ≤ t. We determine the true order of magnitude of the cardinality |ℛ
n
(t)| of the set ℛ
n
(t) by showing that, as t → ∞, t
2 log t ≪ |ℛ2(t)| ≪ t
2 log t and t
n
≪ |ℛ
n
(t)| ≪ t
n
for every fixed n ≥ 3. Further, for 1 < n/2 < k < n fixed let ℛ
k,n
(t) ⊂ ℛ
n
(t) such that p(X) ∈ ℛ
k,n
(t) if and only if p(X) has an irreducible factor in ℤ[X] of degree k. Then, as t → ∞, we always have t
k+1 ≪ |ℛ
k,n
(t)| ≪ t
k+1 and hence |ℛ
n−1,n
(t)| ≫ |ℛ
n
(t)| so that ℛ
n−1,n
(t) is the dominating subclass of ℛ
n
(t) since we can show that |ℛ
n
(t)∖ℛ
n−1,n
(t)| ≪ t
n−1(log t)2.On the contrary, if R
n
s
(t) is the total number of all polynomials in ℛ
n
(t) which split completely into linear factors over ℤ, then t
2(log t)
n−1 ≪ R
n
s
(t) ≪ t
2 (log t)
n−1 (t → ∞) for every fixed n ≥ 2.
相似文献