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1.
Sofiya Ostrovska 《Proceedings Mathematical Sciences》2007,117(4):485-493
Let φ be a power series with positive Taylor coefficients {a
k
}
k=0∞ and non-zero radius of convergence r ≤ ∞. Let ξ
x
, 0 ≤ x < r be a random variable whose values α
k
, k = 0, 1, …, are independent of x and taken with probabilities a
k
x
k
/φ(x), k = 0, 1, ….
The positive linear operator (A
φ
f)(x):= E[f(ξ
x
)] is studied. It is proved that if E(ξ
x
) = x, E(ξ
x
2) = qx
2 + bx + c, q, b, c ∈ R, q > 0, then A
φ
reduces to the Szász-Mirakyan operator in the case q = 1, to the limit q-Bernstein operator in the case 0 < q < 1, and to a modification of the Lupaş operator in the case q > 1. 相似文献
2.
Let F
k
be a free group of rank k ≥ 2 with a fixed set of free generators. We associate to any homomorphism φ from F
k
to a group G with a left-invariant semi-norm a generic stretching factor, λ(φ), which is a noncommutative generalization of the translation number. We concentrate on the situation where φ: F
k
→ Aut(X) corresponds to a free action of F
k
on a simplicial tree X, in particular, where φ corresponds to the action of F
k
on its Cayley graph via an automorphism of F
k
. In this case we are able to obtain some detailed “arithmetic” information about the possible values of λ = λ(φ). We show that λ ≥ 1 and is a rational number with 2kλ ∈ ℤ[1/(2k − 1)] for every φ ∈ Aut(F
k
). We also prove that the set of all λ(φ), where φ varies over Aut(F
k
), has a gap between 1 and 1+(2k−3)/(2k
2−k), and the value 1 is attained only for “trivial” reasons. Furthermore, there is an algorithm which, when given φ, calculates λ(φ).
The second and the third author were supported by the NSF grant DMS#0404991 and the NSA grant DMA#H98230-04-1-0115. 相似文献
3.
Ignacy I. Kotlarski 《Annali di Matematica Pura ed Applicata》1969,83(1):253-260
Summary The probability density functions fk(xk)=Ak|xk|p
k−1 e−aφ
k(xk) of independent random variables x0, x1, ..., xn, are characterized by independence of two functions of them.
Entrata in Redazione il 12 aprile 1969. 相似文献
4.
Ming-Jun Lai 《Advances in Computational Mathematics》2006,25(1-3):41-56
We propose a constructive method to find compactly supported orthonormal wavelets for any given compactly supported scaling
function φ in the multivariate setting. For simplicity, we start with a standard dilation matrix 2I2×2 in the bivariate setting and show how to construct compactly supported functions ψ1,. . .,ψn with n>3 such that {2kψj(2kx−ℓ,2ky−m), k,ℓ,m∈Z, j=1,. . .,n} is an orthonormal basis for L2(ℝ2). Here, n is dependent on the size of the support of φ. With parallel processes in modern computer, it is possible to use these orthonormal
wavelets for applications. Furthermore, the constructive method can be extended to construct compactly supported multi-wavelets
for any given compactly supported orthonormal multi-scaling vector. Finally, we mention that the constructions can be generalized
to the multivariate setting.
Dedicated to Professor Charles A. Micchelli on the occasion of his 60th birthday
Mathematics subject classifications (2000) 42C15, 42C30. 相似文献
5.
J. K. Brooks Kazuyuki Saitô JD Maitland Wright 《Rendiconti del Circolo Matematico di Palermo》2003,52(1):5-14
LetA be aC*-algebra with second dualA″. Let (φ
n)(n=1,...) be a sequence in the dual ofA such that limφ
n(a) exists for eacha εA. In general, this does not imply that limφ
n(x) exists for eachx εA″. But if limφ
n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ
n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for
positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem. 相似文献
6.
The concept of absolutely monotone functions is generalized by replacing the conditionsφ
(k)(t)≧0,k=0, 1, … by an infinite sequence of differential inequalitiesφ(t)≧0,L
kφ(t)≧0,k=1, 2, …, where theL
k are differential operators of a special type. It is shown that these functions have a valid series expansion in terms of
basic functions associated with the operatorsL
k. 相似文献
7.
V. Ya. Yakubov 《Differential Equations》2011,47(3):451-452
We consider three families of equations of the form y″ + (1 + φ(x))y = 0, where the coefficient φ(x) satisfies the condition lim
x→+∞
φ(x) = 0. We obtain solutions of these equations in closed form. We show that the maximum absolute values of solutions grow at
the rate of a logarithmic function, a power-law function, and even an exponential function as x → ∞. 相似文献
8.
Xiangsheng Xu 《Rendiconti del Circolo Matematico di Palermo》1991,40(1):69-101
Existence of a weak solution is established for the first boundary value problem for the equation (c(u))
t
=(φ(u
x
)
x
in the case wherec′(x), φ′(x) may oscillate near zero,c′(x), φ′(x) may be unbounded above, andc′(x), φ′(x) may not be bounded away from zero asx→0. Some regularity properties of the wea, solution are also obtained. 相似文献
9.
We show, conditional on a uniform version of the prime k-tuples conjecture, that there are x/(log x)1+o(1) numbers not exceeding x common to the ranges of φ and σ. Here φ is Euler’s totient function and σ is the sum-of-divisors function. 相似文献
10.
Let Ω ⊆ ℝn be a bounded convex domain with C
2 boundary. For 0 < p, q ⩽ ∞ and a normal weight φ, the mixed norm space H
k
p,q,φ
(Ω) consists of all polyharmonic functions f of order k for which the mixed norm ∥ · ∥p,q,φ < ∞. In this paper, we prove that the Gleason’s problem (Ω, a, H
k
p,q,φ
) is always solvable for any reference point a ∈ Ω. Also, the Gleason’s problem for the polyharmonic φ-Bloch (little φ-Bloch) space is solvable. The parallel results for the hyperbolic harmonic mixed norm space are obtained. 相似文献
11.
V. Yu. Protasov 《Functional Analysis and Its Applications》2011,45(1):46-55
We study continuous subadditive set-valued maps taking points of a linear space X to convex compact subsets of a linear space Y. The subadditivity means that φ(x
1 + x
2) ⊂ φ(x
1) + φ(x
2). We characterize all pairs of locally convex spaces (X, Y) for which any such map has a linear selection, i.e., there exists a linear operator A: X → Y such that Ax ∈ φ(x), x ∈ X. The existence of linear selections for a class of subadditive maps generated by differences of a continuous function is
proved. This result is applied to the Lipschitz stability problem for linear operators in Banach spaces. 相似文献
12.
H. S. Özarslan 《Proceedings Mathematical Sciences》2003,113(2):165-169
In this paper, by using an almost increasing and δ-quasi-monotone sequence, a general theorem on φ- | C, α |
k summability factors, which generalizes a result of Bor [3] on φ |C, 1|
k summability factors, has been proved under weaker and more general conditions. 相似文献
13.
BinodChandraTripathy SabitaMahanta 《应用数学学报(英文版)》2004,20(3):487-494
In this article we introduce the vector valued sequence space m(E_k,φ,∧),associated with themultiplier sequence ∧=(λ_k) of non-zero complex numbers,and the terms of the sequence are chosen from theseminormed spaces E_k,seminormed by f_k for all k∈N.This generalizes the sequence space m(φ) introducedand studied by Sargent.We study some of its properties like solidity,completeness,and obtain some inclusionresults.We also characterize the multiplier problem and obtain the corresponding spaces dual to m(E_k,φ,∧).We prove some general results too. 相似文献
14.
Let λ and μ be solid sequence spaces. For a sequence of modulus functions Φ = (ϕ k) let λ(Φ) = {x = (x
k
): (ϕk(|x
k
|)) ∈ λ}. Given another sequence of modulus functions Ψ = (ψk), we characterize the continuity of the superposition operators P
f
from λ(Φ) into μ (Ψ) for some Banach sequence spaces λ and μ under the assumptions that the moduli ϕk (k ∈ ℕ) are unbounded and the topologies on the sequence spaces λ(Φ) and μ(Ψ) are given by certain F-norms. As applications
we consider superposition operators on some multiplier sequence spaces of Maddox type.
This research was supported by Estonian Science Foundation Grant 5376. 相似文献
15.
V. V. Arestov 《Ukrainian Mathematical Journal》2010,62(3):331-342
We investigate the problem of algebraic polynomials with given leading coefficients that deviate least from zero on the segment
[–1, 1] with respect to a measure, or, more precisely, with respect to the functional μ(f) = mes{x ∈ [–1, 1]: ∣f (x)∣ ≥ 1}. We also discuss an analogous problem with respect to the integral functionals ∫–11 φ (∣f (x)∣) dx for functions φ that are defined, nonnegative, and nondecreasing on the semiaxis [0, +∞). 相似文献
16.
YANG Shouzhi & PENG Lizhong Department of Mathematics Shantou University Shantou China LMAM School of Mathematical Sciences Peking University Beijing China 《中国科学A辑(英文版)》2006,49(1):86-97
An algorithm is presented for raising an approximation order of any given orthogonal multiscaling function with the dilation factor a. Let φ(x) = [φ1(x),φ2(x),…,φr(x)]T be an orthogonal multiscaling function with the dilation factor a and the approximation order m. We can construct a new orthogonal multiscaling function φnew(x) = [ φT(x). f3r 1(x),φr 2(x),…,φr s(x)}T with the approximation order m L(L ∈ Z ). In other words, we raise the approximation order of multiscaling function φ(x) by increasing its multiplicity. In addition, we discuss an especial setting. That is, if given an orthogonal multiscaling function φ(x) = [φ1 (x), φ2(x), …, φr(x)]T is symmetric, then the new orthogonal multiscaling function φnew(x) not only raise the approximation order but also preserve symmetry. Finally, some examples are given. 相似文献
17.
In this paper, based on existing symmetric multiwavelets, we give an explicit algorithm for constructing multiwavelets with high approximation order and symmetry. Concretely, suppose Φ(x) := (φ1(x), . . . , φr(x))T is a symmetric refinable function vectors with approximation order m. For an arbitrary nonnegative integer n, a new symmetric refinable function vector Φnew(x) := (φn1 ew(x), . . . , φrn ew(x))T with approximation order m + n can be constructed through the algorithm mentioned above. Additionally,... 相似文献
18.
A class function φ on a finite group G is said to be an order separator if, for every x and y in G \ {1}, φ(x) = φ(y) is equivalent to x and y being of the same order. Similarly, φ is said to be a class-size separator if, for every x and y in G\ {1}, φ(x) = φ(y) is equivalent to |C
G
(x)| = |C
G
(y)|. In this paper, finite groups whose nonlinear irreducible complex characters are all order separators (respectively, class-size
separators) are classified. In fact, a more general setting is studied, from which these classifications follow. This analysis
has some connections with the study of finite groups such that every two elements lying in distinct conjugacy classes have
distinct orders, or, respectively, in which disctinct conjugacy classes have distinct sizes.
Received: 10 April 2007 相似文献
19.
V. S. Atabekyan 《Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences)》2010,45(2):112-122
In the present paper for arbitrary automorphism φ of the free Bunside group B(m, n) and for any odd number n ≥ 1003 a sufficient condition for existence of non-φ-admissible normal subgroup of B(m, n) was found. In particular, if automorphism φ is normal, then for any basis {a
1, a
2, …, a
m
} of the group B(m, n) there is an integer k such that for each i the elements a
i
and φ(a
i)
k
are conjugates. 相似文献
20.
Let Λℝ denote the linear space over ℝ spanned by z
k
, k∈ℤ. Define the real inner product 〈⋅,⋅〉
L
:Λℝ×Λℝ→ℝ,
, N∈ℕ, where V satisfies: (i) V is real analytic on ℝ∖{0}; (ii) lim
|
x
|→∞(V(x)/ln (x
2+1))=+∞; and (iii) lim
|
x
|→0(V(x)/ln (x
−2+1))=+∞. Orthogonalisation of the (ordered) base
with respect to 〈⋅,⋅〉
L
yields the even degree and odd degree orthonormal Laurent polynomials (OLPs)
: φ
2n
(z)=∑
k=−n
n
ξ
k
(2n)
z
k
, ξ
n
(2n)>0, and φ
2n+1(z)=∑
k=−n−1
n
ξ
k
(2n+1)
z
k
, ξ
−n−1(2n+1)>0. Associated with the even degree and odd degree OLPs are the following two pairs of recurrence relations: z
φ
2n
(z)=c
2n
♯
φ
2n−2(z)+b
2n
♯
φ
2n−1(z)+a
2n
♯
φ
2n
(z)+b
2n+1
♯
φ
2n+1(z)+c
2n+2
♯
φ
2n+2(z) and z
φ
2n+1(z)=b
2n+1
♯
φ
2n
(z)+a
2n+1
♯
φ
2n+1(z)+b
2n+2
♯
φ
2n+2(z), where c
0
♯
=b
0
♯
=0, and c
2k
♯
>0, k∈ℕ, and z
−1
φ
2n+1(z)=γ
2n+1
♯
φ
2n−1(z)+β
2n+1
♯
φ
2n
(z)+α
2n+1
♯
φ
2n+1(z)+β
2n+2
♯
φ
2n+2(z)+γ
2n+3
♯
φ
2n+3(z) and z
−1
φ
2n
(z)=β
2n
♯
φ
2n−1(z)+α
2n
♯
φ
2n
(z)+β
2n+1
♯
φ
2n+1(z), where β
0
♯
=γ
1
♯
=0, β
1
♯
>0, and γ
2l+1
♯
>0, l∈ℕ. Asymptotics in the double-scaling limit N,n→∞ such that N/n=1+o(1) of the coefficients of these two pairs of recurrence relations, Hankel determinant ratios associated with the real-valued,
bi-infinite strong moment sequence
, and the products of the (real) roots of the OLPs are obtained by formulating the even degree and odd degree OLP problems
as matrix Riemann-Hilbert problems on ℝ, and then extracting the large-n behaviours by applying the non-linear steepest-descent method introduced in (Ann. Math. 137(2):295–368, [1993]) and further developed in (Commun. Pure Appl. Math. 48(3):277–337, [1995]) and (Int. Math. Res. Not. 6:285–299, [1997]).
相似文献