共查询到20条相似文献,搜索用时 31 毫秒
1.
The product ϕ
λ
(α,β)
(t1)ϕ
λ
(α,β)
(t2) of two Jacobi functions is expressed as an integral in terms of ϕ
λ
(α,β)
(t3) with explicit non-negative kernel, when α≧β≧−1/2. The resulting convolution structure for Jacobi function expansions is
studied. For special values of α and β the results are known from the theory of symmetric spaces. 相似文献
2.
M. Ivette Gomes 《Annals of the Institute of Statistical Mathematics》1984,36(1):71-85
Summary Let {X
n}n≧1 be a sequence of independent, identically distributed random variables. If the distribution function (d.f.) ofM
n=max (X
1,…,X
n), suitably normalized with attraction coefficients {αn}n≧1(αn>0) and {b
n}n≧1, converges to a non-degenerate d.f.G(x), asn→∞, it is of interest to study the rate of convergence to that limit law and if the convergence is slow, to find other d.f.'s
which better approximate the d.f. of(M
n−bn)/an thanG(x), for moderaten. We thus consider differences of the formF
n(anx+bn)−G(x), whereG(x) is a type I d.f. of largest values, i.e.,G(x)≡Λ(x)=exp (-exp(−x)), and show that for a broad class of d.f.'sF in the domain of attraction of Λ, there is a penultimate form of approximation which is a type II [Ф
α(x)=exp (−x−α), x>0] or a type III [Ψ
α(x)= exp (−(−x)α), x<0] d.f. of largest values, much closer toF
n(anx+bn) than the ultimate itself. 相似文献
3.
Leopold Flatto 《Israel Journal of Mathematics》1973,15(2):167-184
LetN
α, m equal the number of randomly placed arcs of length α (0<α<1) required to cover a circleC of unit circumferencem times. We prove that limα→0
P(Nα,m≦(1/α) (log (1/α)+mlog log(1/α)+x)=exp ((−1/(m−1)!) exp (−x)). Using this result for m=1, we obtain another derivation of Steutel's resultE(Nα,1)=(1/α) (log(1/α)+log log(1/α)+γ+o(1)) as α→0, γ denoting Euler's constant. 相似文献
4.
Letϕ: [0, 1]→R have continuous derivativeon the closed interval [0, 1], ∫
0
1
ϕ(x)dx=0, and letα be irrational. Ifϕ(1) ≠ϕ(0), then (x, y) ↦ (x + α, y + ϕ (x)) is ergodic onR/Z ×R. 相似文献
5.
A. F. Izé 《Annali di Matematica Pura ed Applicata》1973,96(1):21-39
Summary It is studied the relationship between the solutions of the linear functional differential equations(1) (d/dx) D(xt)=L(xt) and its perturbed equation(2) [(d/dx) D(xt)−G(t, xt)]= =L(xt)+F(t, xt) and is proved, under certain hypotheses which will be precised bellow that, if μ is a simple characteristic root of(1), then there exist a σ > 0 and a non zero vector a such that system(2) has a solution satisfying
where δ(t)=αd{F(t, ϕμ)+μG(t, ϕμ)+F(t, X0G(t, ϕμ))}, ϕμ(θ)=c·exp (μθ), −r⩾θ⩾0 and α, d, X0 are given constants.
Entrata in Redazione il 5 gennaio 1972. 相似文献
6.
A refinable function φ(x):ℝn→ℝ or, more generally, a refinable function vector Φ(x)=[φ1(x),...,φr(x)]T is an L1 solution of a system of (vector-valued) refinement equations involving expansion by a dilation matrix A, which is an expanding
integer matrix. A refinable function vector is called orthogonal if {φj(x−α):α∈ℤn, 1≤j≤r form an orthogonal set of functions in L2(ℝn). Compactly supported orthogonal refinable functions and function vectors can be used to construct orthonormal wavelet and
multiwavelet bases of L2(ℝn). In this paper we give a comprehensive set of necessary and sufficient conditions for the orthogonality of compactly supported
refinable functions and refinable function vectors. 相似文献
7.
Angelo Tonolo 《Annali di Matematica Pura ed Applicata》1960,50(1):127-133
Sunto Per la funzione reale del punto P(x, y): F[ξ(P), η(P)], ove u=ξ(P), v=η(P) sono implicitamente definite nel campo reale dal
sistema delle due equazioni u−x+ϕ(u, v)=0, v−y+φ(u, v)=0 si dà uno sviluppo che estende quello ottenuto dalLevi-Civita per la funzione F[y(x)], ove y(x) è definita dalla equazione y−x+ϕ(y)=0.
Ad Antonio Signorini nel suo 70mo compleanno. 相似文献
8.
Min Guohua 《分析论及其应用》1992,8(3):28-37
In this paper, the Lp-convergence of Grünwald interpolation Gn(f,x) based on the zeros of Jacobi polynomials J
n
(α,β)
(x)(−1<α,β<1) is considered. Lp-convergence (0<p<2) of Grünwald interpolation Gn(f,x) is proved for p·Max(α,β)<1. Moreover, Lp-convergence (p>0) of Gn(f,x) is obtained for −1<α,β≤0. Therefore, the results of [1] and [3–5] are improved. 相似文献
9.
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
10.
Ante Mimica 《Potential Analysis》2010,32(3):275-303
In this paper we prove Harnack inequality for nonnegative functions which are harmonic with respect to random walks in ℝ
d
. We give several examples when the scale invariant Harnack inequality does not hold. For any α ∈ (0,2) we also prove the Harnack inequality for nonnegative harmonic functions with respect to a symmetric Lévy process
in ℝ
d
with a Lévy density given by $c|x|^{-d-\alpha}1_{\{|x|\leq 1\}}+j(|x|)1_{\{|x|>1\}}$c|x|^{-d-\alpha}1_{\{|x|\leq 1\}}+j(|x|)1_{\{|x|>1\}}, where 0 ≤ j(r) ≤ cr
− d − α
, ∀ r > 1, for some constant c. Finally, we establish the Harnack inequality for nonnegative harmonic functions with respect to a subordinate Brownian motion
with subordinator with Laplace exponent ϕ(λ) = λ
α/2ℓ(λ), λ > 0, where ℓ is a slowly varying function at infinity and α ∈ (0,2). 相似文献
11.
E. I. Pancheva 《Journal of Mathematical Sciences》2000,99(3):1306-1316
Let g be the distribution function (d.f.) of an extremal process Y. If g is invariant with respect to a continuous one-parameter
group of time-space changes {ηα = (τα, Lα): α > 0}, i.e. g ∘ ηα = g ∀ α > 0, then g is self-similar. If g is invariant w.r.t. the cyclic group {η∘(n), n ∈Z} of a time-space change ν, then g is semi-self-similar. The semi-self-similar extremal processes are limiting for sequences
of extremal processes Yn(t)=L
n
−1
∘ Y ∘ τn (t) if going along a geometrically increasing subsequence kn ∼ ϕn, ϕ > 1, n → ∞. The main properties of multivariate semi-self-similar extremal processes and some examples are discussed in
the paper. The results presented are an analog of the theory of semi-self-similar processes with additive increments developed
by Maejima and Sato in 1997.
Supported by the Bulgarian Ministry of Education and Science (grant No. MM-705/97).
Proceedings of the Seminar on Stability Problems for Stochastic Models, Vologda, Russia, 1998, Part I. 相似文献
12.
T. Akhobadze 《Acta Mathematica Hungarica》2011,130(3):286-308
In 1953 Nash [7] introduced the class of functions Φ. In this paper the behaviour of generalized Cesàro (C,α
n
)-means (α
n
∈(−1,0)) of trigonometric Fourier series of the classes H
ω
∩Φ in the space of continuous functions is studied. The sharpness of the results obtained is shown. 相似文献
13.
In this paper we deal with the limit behaviour of the bounded solutions uε of quasi-linear equations of the form
of Ω with Dirichlet boundary conditions on σΩ. The map a=a(x,ϕ) is periodic in x, monotone in ϕ, and satisfies suitable coerciveness
and growth conditions. The function H=H(x,s,ϕ) is assumed to be periodic in x, continuous in [s,ϕ] and to grow at most like
|ξ|p. Under these assumptions on a and H we prove that there exists a function H0=H0(s,ϕ) with the same behaviour of H, such that, up to a subsequence, (uε) converges to a solution u of the homogenized problem -div(b(Du)) + γ|u|p-2u = H0(u,Du) + h(x) on Ω, where b depends only on a and has analogous qualitative properties. 相似文献
14.
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
15.
W. D. Banks F. Luca F. Saidak P. StĂ;nicĂ 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2005,75(1):215-244
Let ϕ and λ be the Euler and Carmichael functions, respectively. In this paper, we establish lower and upper bounds for the
number of positive integers n ≤ x such that ϕ(λ(n)) = λ(ϕ(n)). We also study the normal order of the function ϕ(λ(n))/λ(ϕ(n)). 相似文献
16.
K. M. D'yakonov 《Journal of Mathematical Sciences》1996,78(2):131-141
Let ϕ be a unimodular function on the unit circle
and let Kp(ϕ) denote the kernel of the Toeplitz operator Tϕ in the Hardy space Hp, p≥1;
. Suppose Kp(ϕ)≠{0}. The problem is to find out how the smoothness of the symbol ϕ influences the boundary smoothness of functions in
Kp(ϕ). One of the main results is as follows.
Theorem 1 Let 1<p, q<+∞, 1<r≤+∞, q−1=p−1+r−1. Suppose |ϕ|≡1 on
and ϕ∈W
r
1
(i.e.,
). Then Kp(ϕ)⊂W
q
1
. Moreover, for any f∈Kp(ϕ) we have ‖f′‖q≤c(p, r)‖ϕ′‖r ‖f‖. Bibliography: 19 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 201, 1992, pp. 5–21.
Translated by K. M. D'yakonov. 相似文献
17.
On weighted approximation by Bernstein-Durrmeyer operators 总被引:6,自引:0,他引:6
Zhang Zhenqiu 《分析论及其应用》1991,7(2):51-64
In this paper, we consider weighted approximation by Bernstein-Durrmeyer operators in Lp[0, 1] (1≤p≤∞), where the weight function w(x)=xα(1−x)β,−1/p<α, β<1-1/p. We obtain the direct and converse theorems. As an important tool we use appropriate K-functionals.
Supported by Zhejiang Provincial Science Foundation. 相似文献
18.
Joseph Weier 《Annali dell'Universita di Ferrara》1958,8(1):29-37
Riassunto SeM edN sono varietà poliedriche chiuse connesse ed orientate di dimensioni rispettivem edn, conm≥n>2, edf∶M→N è una trasformazione continua, allora per ognir, minore din e non inferiore a 2, si definisce un omomorfismo indotto ϕrπ:r
(N)→H
m-n+r
(M) dal quale si ricavano certi invarianti topologici.
Résumé Soientm≥n>r≥2 des entiers etM, N des variétés polyédrales closes connexes orientées satisfaisant dimM=m et dimN=n, de plusH i(M) le groupe de Betti à i dimensions deM,M,π i (N) le groupe de Hurewicz ài dimensions deN, etf∶M→N une application continue. Alorsf définit, pour,r=2, 3, …n−1, un homomorphisme réciproque ϕrπ:r (N)→H m-n+r (M) comme il suit. Etant donné un élément α du groupe πr (N) et uner-sphère continue orientéeS de α, on peut supposer quef −1(S) soit un polyèdre finiA àm−n+r dimensions. Parf est induit dansA un (m−n+r)-cyclez à coefficients entiers, et la classe d'homologie dez est justement l'image ϕr(α) de α par ϕr. Pourr=1, on obtient un homomorphisme réciproque ϕrπ:r (N)→H m-n+r (M) du groupe fondamentalF(N) deN dans le groupe d'homologie àm−n+1 dimensions deM. A l'aide des homomorphismes ϕ,,ϕ2,ϕ,3...,ϕn-i, on parvient à certaines expressions caractéristiques dépendantes seulement de la classe d'homotopie def, en particulier on obtient des constantes pour les images des bases de Betti deM, pour Fimage du groupe de torsion deM, et pour l'image réciproque du groupe fondamental deN.相似文献
19.
Oscar F. Bandtlow 《Integral Equations and Operator Theory》2008,61(1):21-43
For a, α > 0 let E(a, α) be the set of all compact operators A on a separable Hilbert space such that s
n
(A) = O(exp(-anα)), where s
n
(A) denotes the n-th singular number of A. We provide upper bounds for the norm of the resolvent (zI − A)−1 of A in terms of a quantity describing the departure from normality of A and the distance of z to the spectrum of A. As a consequence we obtain upper bounds for the Hausdorff distance of the spectra of two operators in E(a, α).
相似文献
20.
T. Shibata 《Annali di Matematica Pura ed Applicata》2007,186(3):525-537
We consider the nonlinear Sturm–Liouville problem
where λ > 0 is an eigenvalue parameter. To understand well the global behavior of the bifurcation branch in R
+ × L
2(I), we establish the precise asymptotic formula for λ(α), which is associated with eigenfunction u
α with ‖ u
α ‖2 = α, as α → ∞. It is shown that if for some constant p > 1 the function h(u) ≔ f(u)/u
p
satisfies adequate assumptions, including a slow growth at ∞, then λ(α) ∼ α
p−1
h(α) as α → ∞ and the second term of λ(α) as α → ∞ is determined by lim
u → ∞
uh′(u).
Mathematics Subject Classification (2000) 34B15 相似文献
(1) |