共查询到20条相似文献,搜索用时 137 毫秒
1.
Fabio Scarabotti 《The Ramanujan Journal》2011,25(1):57-91
We develop a tree method for multidimensional q-Hahn polynomials. We define them as eigenfunctions of a multidimensional q-difference operator and we use the factorization of this operator as a key tool. Then we define multidimensional q-Racah polynomials as the connection coefficients between different bases of q-Hahn polynomials. We show that our multidimensional q-Racah polynomials may be expressed as product of ordinary one-dimensional q-Racah polynomial by means of a suitable sequence of transplantations of edges of the trees. Our paper is inspired to the
classical tree methods in the theory of Clebsch–Gordan coefficients and of hyperspherical coordinates. It is based on previous
work of Dunkl, who considered two-dimensional q-Hahn polynomials. It is also related to a recent paper of Gasper and Rahman: we show that their multidimensional q-Racah polynomials correspond to a particular case of our construction. 相似文献
2.
In this paper, we study the weighted (x(q + 1), x; 2, q)-minihypers. These are weighted sets of x(q + 1) points in PG(2, q) intersecting every line in at least x points. We investigate the decomposability of these minihypers, and define a switching construction which associates to an
(x(q + 1), x; 2, q)-minihyper, with x ≤ q
2 − q, not decomposable in the sum of another minihyper and a line, a (j(q + 1), j; 2, q)-minihyper, where j = q
2 − q − x, again not decomposable into the sum of another minihyper and a line. We also characterize particular (x(q + 1), x; 2, q)-minihypers, and give new examples. Additionally, we show that (x(q + 1), x; 2, q)-minihypers can be described as rational sums of lines. In this way, this work continues the research on (x(q + 1), x; 2, q)-minihypers by Hill and Ward (Des Codes Cryptogr 44:169–196, 2007), giving further results on these minihypers. 相似文献
3.
We study the “q-commutative” power series ring R: = k
q
[[x
1,...,x
n
]], defined by the relations x
i
x
j
= q
ij
x
j
x
i
, for mulitiplicatively antisymmetric scalars q
ij
in a field k. Our results provide a detailed account of prime ideal structure for a class of noncommutative, complete, local, noetherian
domains having arbitrarily high (but finite) Krull, global, and classical Krull dimension. In particular, we prove that the
prime spectrum of R is normally separated and is finitely stratified by commutative noetherian spectra. Combining this normal separation with
results of Chan, Wu, Yekutieli, and Zhang, we are able to conclude that R is catenary. Following the approach of Brown and Goodearl, we also show that links between prime ideals are provided by canonical
automorphisms. Moreover, for sufficiently generic q
ij
, we find that R has only finitely many prime ideals and is a UFD (in the sense of Chatters). 相似文献
4.
In the study of differential equations on [ − 1,1] subject to linear homogeneous boundary conditions of finite order, it is
often expedient to represent the solution in a Galerkin expansion, that is, as a sum of basis functions, each of which satisfies
the given boundary conditions. In order that the functions be maximally distinct, one can use the Gram-Schmidt method to generate
a set orthogonal with respect to a particular weight function. Here we consider all such sets associated with the Jacobi weight
function, w(x) = (1 − x)
α
(1 + x)
β
. However, this procedure is not only cumbersome for sets of large degree, but does not provide any intrinsic means to characterize
the functions that result. We show here that each basis function can be written as the sum of a small number of Jacobi polynomials,
whose coefficients are found by imposing the boundary conditions and orthogonality to the first few basis functions only.
That orthogonality of the entire set follows—a property we term “auto-orthogonality”—is remarkable. Additionally, these basis
functions are shown to behave asymptotically like individual Jacobi polynomials and share many of the latter’s useful properties.
Of particular note is that these basis sets retain the exponential convergence characteristic of Jacobi expansions for expansion
of an arbitrary function satisfying the boundary conditions imposed. Further, the associated error is asymptotically minimized
in an L
p(α) norm given the appropriate choice of α = β. The rich algebraic structure underlying these properties remains partially obscured by the rather difficult form of the
non-standard weighted integrals of Jacobi polynomials upon which our analysis rests. Nevertheless, we are able to prove most
of these results in specific cases and certain of the results in the general case. However a proof that such expansions can
satisfy linear boundary conditions of arbitrary order and form appears extremely difficult. 相似文献
5.
María J. Carro 《Mathematische Zeitschrift》2007,255(4):813-825
Given a sublinear operator T such that is bounded, it can be shown that is bounded, with constant C/(1−q), for every 0 < q < 1. In this paper, we study the converse result, not only for sequence spaces, but for general measure spaces proving that,
if T : L
q
(μ) → X is bounded, with constant C/(1−q), for every and X is Banach, then T : L log (1/L)(μ) → X is bounded. Moreover, this result is optimal. We also show that things are quite different if the Banach condition on X is dropped.
This work has been partially supported by MTM2004-02299 and by 2005SGR00556. 相似文献
6.
Nazim Mahmudov 《Numerical Algorithms》2010,53(4):439-450
In this note we give the estimates of the central moments for q-Bernstein operators (0 < q < 1) which can be used for studying the approximation properties of the operators. 相似文献
7.
Given 1≤ p,q < ∞, let BLpLq be the class of all Banach lattices X such that X is isometrically lattice isomorphic to a band in some Lp(Lq)-Banach lattice. We show that the range of a positive contractive projection on any BLpLq-Banach lattice is itself in BLpLq. It is a consequence of this theorem and previous results that BLpLq is first-order axiomatizable in the language of Banach lattices. By studying the pavings of arbitrary BLpLq-Banach lattices by finite dimensional sublattices that are themselves in this class, we give an explicit set of axioms for
BLpLq. We also consider the class of all sublattices of Lp(Lq)-Banach lattices; for this class (when p/q is not an integer) we give a set of axioms that are similar to Krivine’s well-known axioms for the subspaces of Lp-Banach spaces (when p/2 is not an integer). We also extend this result to the limiting case q = ∞. 相似文献
8.
V. N. Kublanovskaya 《Journal of Mathematical Sciences》2011,176(1):93-101
The method of hereditary pencils, originally suggested by the author for solving spectral problems for two-parameter matrices
(pencils of matrices), is extended to the case of q-parameter, q ≥ 2, polynomial matrices. Algorithms for computing points of the finite regular and singular spectra of a q-parameter polynomial matrix and their theoretical justification are presented. Bibliography: 2 titles. 相似文献
9.
In this paper, we introduce the concept of (1, 1)-q-coherent pair of linear functionals (U,V)(\mathcal{U},\mathcal{V}) as the q-analogue to the generalized coherent pair studied by Delgado and Marcellán in (Methods Appl Anal 11(2):273–266, 2004). This means that their corresponding sequences of monic orthogonal polynomials {P
n
(x)}
n ≥ 0 and {R
n
(x)}
n ≥ 0 satisfy
\frac(DqPn+1)(x)[n+1]q + an\frac(DqPn)(x)[n]q = Rn(x) + bnRn-1(x) , an 1 0, n 3 1, \frac{\left(D_qP_{n+1}\right)(x)}{[n+1]_q} + a_{n}\frac{\left(D_qP_{n}\right)(x)}{[n]_q} = R_{n}(x) + b_{\!n}R_{n-1}(x) \,, \quad\, a_{n}\neq0,\,\, n\geq1, 相似文献
10.
Young-Tak Oh 《Mathematische Zeitschrift》2007,257(1):151-191
In this paper, we construct a q-deformation of the Witt-Burnside ring of a profinite group over a commutative ring, where q ranges over the set of integers. When q = 1, it coincides with the Witt-Burnside ring introduced by Dress and Siebeneicher (Adv. Math. 70, 87–132 (1988)). To achieve
our goal we first show that there exists a q-deformation of the necklace ring of a profinite group over a commutative ring. As in the classical case, i.e., the case q = 1, q-deformed Witt-Burnside rings and necklace rings always come equipped with inductions and restrictions. We also study their
properties. As a byproduct, we prove a conjecture due to Lenart (J. Algebra. 199, 703-732 (1998)). Finally, we classify up to strict natural isomorphism in case where G is an abelian profinite group.
The author gratefully acknowledges support from the following grants: KOSEF Grant # R01-2003-000-10012-0; KRF Grant # 2006-331-C00011. 相似文献
11.
In this paper, we consider the zero distributions of q-shift difference polynomials of meromorphic functions with zero order, and obtain two theorems that extend the classical
Hayman results on the zeros of differential polynomials to q-shift difference polynomials. We also investigate the uniqueness problem of q-shift difference polynomials that share a common value. 相似文献
12.
Paola De Vito 《Ricerche di matematica》2011,60(1):39-43
We prove that if q = p
h
, p a prime, do not exist sets U í AG(n,q){U {\subseteq} AG(n,q)}, with |U| = q
k
and 1 < k < n, determining N directions where
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