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1.
We show that the only orthogonal polynomials satisfying a q-difference equation of the form π(x)D
q
P
n
(x) = (α
n
x + β
n
)P
n
(x) + γ
n
P
n−1(x) where π(x) is a polynomial of degree 2, are the Al-Salam Carlitz 1, little and big q-Laguerre, the little and big q-Jacobi, and the q-Bessel polynomials. This is a q-analog of the work carried out in [1].
2000 Mathematics Subject Classification Primary—33C45, 33D45 相似文献
2.
A. I. Kozko 《Journal of Mathematical Sciences》2006,139(6):7151-7164
We study the problem on the completeness of orthogonal systems in asymmetric spaces with sign-sensitive weight. Theorems of
general form are obtained. In particular, the necessary and sufficient conditions on α, β, q
1, and q
2 for which the known orthogonal systems are everywhere dense in asymmetric spaces L
(α,β);q ([0, 1]) are found.
Theorem. Let α, β, q
1, q
2 ∈ [1,+∞]. The following orthogonal systems are dense in asymmetric spaces L
(α,β);q ([0, 1]) if and only if either max{α, β, q
1, q
2} < + ∞ or max {α, β} < +∞, q
1 = q
2 = +∞: trigonometric, algebraic, Haar’s system, Meyer’s system of wavelets, Shannon-Kotel’nikov wavelets, Stromberg and Lemarie-Battle
wavelets, the Walsh system, and the Franklin system.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 24, Dynamical
Systems and Optimization, 2005. 相似文献
3.
This is a continuation of our previous work. We classify all the simple ℋq(D
n
)-modules via an automorphismh defined on the set { λ | Dλ ≠ 0}. Whenf
n(q) ≠ 0, this yields a classification of all the simple ℋ
q
(D
n)- modules for arbitrary n. In general ( i. e., q arbitrary), if λ(1) = λ(2),wegivea necessary and sufficient condition ( in terms of some polynomials ) to ensure that the irreducible ℋq,1(B
n
)- module Dλ remains irreducible on restriction to ℋq(D
n
). 相似文献
4.
N. V. Maslova 《Algebra and Logic》2011,50(2):133-145
We give a classification of maximal subgroups of odd index in finite groups whose socle is isomorphic to one of the groups
PSL
n
(q), PSU
n
(q), or PSp
n
(q) for n ≥ 13. 相似文献
5.
Sur la singularité des produits de Riesz et des mesures spectrales associées à la somme des chiffres
M. Queffelec 《Israel Journal of Mathematics》1979,34(4):337-342
Using a property of generalized characters, we first prove that two Riesz products with constant coefficients and distinct
Fourier spectra are mutually singular. IfS
r
(n) denotes the sum of digits in ther-adic representation of the integern, the same technique allows us to establish the mutual singularity of the spectral measures of the sequences: α(n)=exp[2iπaS
p
(n)],β(n)=exp[2iπbS
q
(n)], for every pair of integersp≠q, a, b being real numbers such thata(p−1)∉ {tiZ} andb(q−1)∉Z. This result has been proved by T. Kamae whenp andq are two relatively prime integers.
相似文献
6.
We consider a class of fourth-order nonlinear difference equations of the form {fx006-01} where α, β are ratios of odd positive integers and {p
n}, {q
n} are positive real sequences defined for all n ∈ ℕ(n
0). We establish necessary and sufficient conditions for the existence of nonoscillatory solutions with specific asymptotic
behavior under suitable combinations of convergence or divergence conditions for the sums {fx006-02}.
Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 1, pp. 8–27, January, 2008. 相似文献
7.
In this paper, we prove the commutator T
b
generated by the strongly singular integral operator T and the function b is bounded from L
p
(w) to L
q
(w
1−q
) if and only if b ∈ Lip
β
(w), where w ∈ A
1, 0 < β < 1, 1 < p < n/β and 1/q = 1/p − β/n. To do this, we first show a maximal function estimate for the commutator. 相似文献
8.
Olivier Teulié 《Monatshefte für Mathematik》2002,116(3):313-324
In this paper, we prove that if β1,…, β n are p-adic numbers belonging to an algebraic number field K of degree n + 1 over Q such that 1, β1,…,β n are linearly independent over Z, there exist infinitely many sets of integers (q 0,…, q n ), with q 0 ≠ 0 and
with H = H(q 0,…, q n ). Therefore, these numbers satisfy the p-adic Littlewood conjecture. To obtain this result, we are using, as in the real case by Peck [2], the structure of a group of units of K. The essential argument to obtain the exponent 1/(n-1) (the same as in the real case) is the use of the p-adic logarithm. We also prove that with the same hypothesis, the inequalities
have no integer solution (q 0,…, q n ) with q 0 ≠ 0, if ɛ > 0 is small enough. 相似文献
9.
Klaus Metsch 《Designs, Codes and Cryptography》2011,60(3):277-282
The famous Dembowski-Wagner theorem gives various characterizations of the classical geometric 2-design PG
n-1(n, q) among all 2-designs with the same parameters. One of the characterizations requires that all lines have size q + 1. It was conjectured [2] that this is also true for the designs PG
d
(n, q) with 2 ≤ d ≤ n − 1. We establish this conjecture, hereby improving various previous results. 相似文献
10.
Hei-Chi Chan 《数学学报(英文版)》2011,27(4):625-634
In this paper, we study a certain partition function a(n) defined by Σ
n≥0
a(n)q
n
:= Π
n=1(1 − q
n
)−1(1 − q
2n
)−1. We prove that given a positive integer j ≥ 1 and a prime m ≥ 5, there are infinitely many congruences of the type a(An + B) ≡ 0 (mod m
j
). This work is inspired by Ono’s ground breaking result in the study of the distribution of the partition function p(n). 相似文献
11.
Let n ≥ 2 be a fixed positive integer, q ≥ 3 and c be two integers with (n, q) = (c, q) = 1. We denote by rn(51, 52, C; q) (δ 〈 δ1,δ2≤ 1) the number of all pairs of integers a, b satisfying ab ≡ c(mod q), 1 〈 a ≤δ1q, 1 ≤ b≤δ2q, (a,q) = (b,q) = 1 and nt(a+b). The main purpose of this paper is to study the asymptotic properties of rn (δ1, δ2, c; q), and give a sharp asymptotic formula for it. 相似文献
12.
We derive leading terms in the expansion of ratios of the formB
n+α(nβ)/Bn(nβ) for largen, whereB
n(x) is any one of the Bessel functionsJ
n(x), Yn(x), Hn(x),I
n(x) andK
n(x). 相似文献
13.
We consider a class of hyperbolic 3-orbifoldsO(α/β); the underlying topological space of such an orbifold is the 3-sphere and the singular set is obtained by adding the two
standard (upper and lower) unknotting tunnels to a 2-bridge linkL(α/β) (and associating branching order two to both unknotting tunnels). These 3-orbifolds are extremal with respect to the notion
of Heegaard genus or Heegaard number of 3-orbifolds; it is to be expected that they are also extremal with respect to the
volume, that is the smallest volume hyperbolic 3-orbifolds should belong to this or some closely related class. We show that
an orbifoldO(α/β) has a uniqueD
2-covering by an orbifoldℒ
n(α/β) wose space is the 3-sphere and whose singular set is the same 2-bridge linkL(α/β) used for the construction ofO(α/β); moreoverO(α/β) is hyperbolic if and only ifℒ
n(α/β) is hyperbolic. As the volumes of the orbifoldsℒ
n(α/β) are known resp. can be computed, this allows to compute the volumes of the orbifoldsO(α/β). The problem of computation of volumes remains open for some closely related classes of 3-orbifolds which are also extremal
with respect to the Heegaard genus (for example associating a branching order bigger than two to one or both unknotting tunnels). 相似文献
14.
Frank de Clerck Stefaan de Winter Elisabeth Kuijken Cristina Tonesi 《Designs, Codes and Cryptography》2006,38(2):179-194
We introduce distance-regular (0,α)-reguli and show that they give rise to (0,α)-geometries with a distance-regular point graph. This generalises the SPG-reguli of Thas [14] and the strongly regular (α,β)-reguli of Hamilton and Mathon [9], which yield semipartial geometries and strongly regular (α,β)-geometries, respectively. We describe two infinite classes of examples, one of which is a generalisation of the well-known
semipartial geometry Tn*(B) arising from a Baer subspace PG(n, q) in PG(n, q2).
Research Fellow supported by the Flemish Institute for the Promotion of Scientific and Technological Research in Industry
(IWT), grant no. IWT/SB/13367/Tonesi
Research assistant of the Fund for Scientific Research Flanders (FWO-Vlaanderen). 相似文献
15.
The prime graph of a finite group G is denoted by Γ(G). In this paper as the main result, we show that if G is a finite group such that Γ(G) = Γ(F
4(q)), where q = 2
n
> 2, then G has a unique nonabelian composition factor isomorphic to F
4(q). We also show that if G is a finite group satisfying |G| = |F
4(q)| and Γ(G) = Γ(F
4(q)), where q = 2
n
> 2, then G @ F4(q){G \cong F_4(q)}. As a consequence of our result we give a new proof for a conjecture of Shi and Bi for F
4(q) where q = 2
n
> 2. 相似文献
16.
We present a formula for the Fourier transforms of order statistics in ℝ
n
showing that all these Fourier transforms are equal up to a constant multiple outside the coordinate planes in ℝ
n
.
Fora
1≥...≥a
n≥0 andq>0, denote by ℓ
w,q
n
then-dimensional Lorentz space with the norm ‖(x
1,...,x
n)‖=(a
1(x
1
*
)
q
+...+a
n(x
n
*
)
q
)1/q
, where (x
1
*
,...,x
n
*
) is the non-increasing permutation of the numbers |x
1|,...,|x
n|. We use the above mentioned formula and the Fourier transform criterion of isometric embeddability of Banach spaces intoL
q [10] to prove that, forn≥3 andq≤1, the space ℓ
w,q
n
is isometric to a subspace ofL
q if and only if the numbersa
1,...,a
n form an arithmetic progression. Forq>1, all the numbersa
i must be equal so that ℓ
w,q
n
= ℓ
q
n
. Consequently, the Lorentz function spaceL
w,q(0, 1) is isometric to a subspace ofL
q if and only ifeither 0<q<∞ and the weightw is a constant function (so thatL
w,q=Lq),or q≤1 andw(t) is a decreasing linear function.
Finally, we relate our results to the theory of positive definite functions.
Both authors were supported in part by the NSF Workshop in Linear Analysis and Probability held at Texas A&M University in
August 1993. The work was done during the first author’s visit to Texas A&M University. 相似文献
17.
Andreas Fr?hlich 《Annali dell'Universita di Ferrara》2000,46(1):11-19
We consider weights of Muckenhoupt classA
q, 1<q<∞. For a bounded Lipschitz domain Ω⊂ℝn we prove a compact embedding and a Poincaré inequality in weighted Sobolev spaces. These technical tools allow us to solve
the weak Neumann problem for the Laplace equation in weighted spaces on ℝn, ℝn
+, on bounded and on exterior domains Ω with boundary of classC
1, which will yield the Helmholtz decomposition ofL
ω
q(Ω)n for general ω∈A
q. This is done by transferring the method of Simader and Sohr [4] to the weighted case. Our result generalizes a result of
Farwig and Sohr [2] where the Helmholtz decomposition ofL
ω
p(Ω)n is proved for an exterior domain and weights of Muckenhoupt class without singularities or degeneracies in a neighbourhood
of ϖΩ.
Sunto In questo lavoro consideriamo dei pesi della classe di MuckenhouptA q, 1<q<∞. Per un dominio limitato lipschitziano Ω⊂ℝn, dimostriamo una immersione compatta ed una disuguaglianza di Poincaré in spazi di Sobolev con peso. Questa tecnica ci consente di risolvere il problema debole di Neumann per l’equazione di Laplace in spazi pesati in ℝn, ℝn + in domini limitati ed in domini esterni con frontiera di classeC 1, che conduce alla decomposizione di Helmholtz diL ω q(Ω)n per un qualsiasi ω∈A q. Il risultato è ottenuto trasferendo il metodo di Simader e Sohr [4] al caso pesato. Quello qui presente estende un risultato di Farwig e Sohr [2] dove la decomposizione di Helmholtz diL ω q(Ω)n è dimostrata per domini esterni e pesi della classe di Muckenhoupt privi di singolarità in un intorno di ϖΩ.相似文献
18.
Some infinite family is constructed of orientable three-dimensional closed manifoldsM
n
(p, q), where n ≥ 2, p ≥ 3, 0 < q < p, and (p, q) = 1, such that M
n
(p, q) is an n-fold cyclic covering of the lens space L(p, q) branched over a two-component link. 相似文献
19.
M. Sghaier 《The Ramanujan Journal》2011,26(1):55-67
Let u(β
0) be the regular form fulfilling (u(β
0))2n+1=β
0(u(β
0))2n
,n≥0 where β
0 is an arbitrary complex number in such a way that for β
0=0 one has the symmetric forms. Recently, the second degree symmetric semi-classical forms (when β
0=0) of class s≤1 were determined. In this paper, we determine all the semi-classical forms u(β
0) of class s=1, which are also of second degree when β
0≠0. 相似文献
20.
Bart De Bruyn 《Annals of Combinatorics》2010,14(2):193-209
Let e be one of the following full projective embeddings of a finite dual polar space Δ of rank n ≥ 2: (i) The Grassmann-embedding of the symplectic dual polar space Δ ≅ DW(2n – 1, q); (ii) the Grassmann-embedding of the Hermitian dual polar space Δ ≅ DH(2n – 1, q
2); (iii) the spin-embedding of the orthogonal dual polar space Δ ≅ DQ(2n, q); (iv) the spin-embedding of the orthogonal dual polar space Δ ≅DQ
−(2n + 1, q). Let He{\mathcal{H}_{e}} denote the set of all hyperplanes of Δ arising from the embedding e. We give a method for constructing the hyperplanes of He{\mathcal{H}_{e}} without implementing the embedding e and discuss (possible) applications of the given construction. 相似文献