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1.
The multi-continued fraction expansion of a multi-formal Laurent series is a sequence pair consisting of an index sequence and a multi-polynomial sequence . We denote the set of the different indices appearing infinitely many times in by H, the set of the different indices appearing in by H+, and call |H| and |H+| the first and second levels of , respectively. In this paper, it is shown how the dimension and basis of the linear space over F(z) (F) spanned by the components of are determined by H (H+), and how the components are linearly dependent on the mentioned basis.  相似文献   

2.
Let be a semisimple Lie algebra and a Cartan subalgebra of . Fix . Let be the invariant holonomic system (see [R. Hotta, M. Kashiwara, The invariant holonomic system on a semisimple Lie algebra, Invent. Math. 75 (1984) 327–358]). First we investigate its formal extension . In the sequel we calculate the characteristic variety of some simple quotients of and its Fourier transform .  相似文献   

3.
Let Sym([n]) denote the collection of all permutations of [n]={1,…,n}. Suppose is a family of permutations such that any two of its elements (when written in its cycle decomposition) have at least t cycles in common. We prove that for sufficiently large n, with equality if and only if is the stabilizer of t fixed points. Similarly, let denote the collection of all set partitions of [n] and suppose is a family of set partitions such that any two of its elements have at least t blocks in common. It is proved that, for sufficiently large n, with equality if and only if consists of all set partitions with t fixed singletons, where Bn is the nth Bell number.  相似文献   

4.
The zero sets of (D+a)ng(t) with in the (t,a)-plane are investigated for and .The results are used to determine entire interpolations to functions , which give representations for the best approximation and best one-sided approximation from the class of functions of exponential type η>0 to .  相似文献   

5.
We prove the relative asymptotic behavior for the ratio of two sequences of multiple orthogonal polynomials with respect to the Nikishin systems of measures. The first Nikishin system is such that for each k, σk has a constant sign on its compact support consisting of an interval , on which almost everywhere, and a discrete set without accumulation points in . If denotes the smallest interval containing , we assume that ΔkΔk+1=0/, k=1,…,m−1. The second Nikishin system is a perturbation of the first by means of rational functions rk, k=1,…,m, whose zeros and poles lie in .  相似文献   

6.
We determine the exact asymptotic behaviour of entropy and approximation numbers of the limiting restriction operator , defined by J(f)=f|Ω. Here Ω is a non-empty bounded domain in , ψ is an increasing slowly varying function, , and is the Besov space of generalized smoothness given by the function tsψ(t). Our results improve and extend those established by Leopold [Embeddings and entropy numbers in Besov spaces of generalized smoothness, in: Function Spaces, Lecture Notes in Pure and Applied Mathematics, vol. 213, Marcel Dekker, New York, 2000, pp. 323–336].  相似文献   

7.
Let be the usual Sobolev class of functions on the unit ball in , and be the subclass of all radial functions in . We show that for the classes and , the orders of best approximation by polynomials in coincide. We also obtain exact orders of best approximation in of the classes by ridge functions and, as an immediate consequence, we obtain the same orders in for the usual Sobolev classes .  相似文献   

8.
Jiaqun Wei   《Journal of Algebra》2007,310(2):903-916
We give conditions under which an n-star module extends to an n-star module, or an n-tilting module, over a ring extension R of A. In case that R is a split extension of A by Q, we obtain that is a 1-tilting module (respectively, a 1-star module) if and only if is a 1-tilting module (respectively, a 1-star module) and generates both and (respectively, generates ), where is an injective cogenerator in the category of all left A-modules. These extend results in [I. Assem, N. Marmaridis, Tilting modules over split-by-nilpotent extensions, Comm. Algebra 26 (1998) 1547–1555; K.R. Fuller, *-Modules over ring extensions, Comm. Algebra 25 (1997) 2839–2860] by removing the restrictions on R and Q.  相似文献   

9.
The well-known density theorem for one-dimensional Gabor systems of the form , where , states that a necessary and sufficient condition for the existence of such a system whose linear span is dense in , or which forms a frame for , is that the density condition is satisfied. The main goal of this paper is to study the analogous problem for Gabor systems for which the window function g vanishes outside a periodic set which is -shift invariant. We obtain measure-theoretic conditions that are necessary and sufficient for the existence of a window g such that the linear span of the corresponding Gabor system is dense in L2(S). Moreover, we show that if this density condition holds, there exists, in fact, a measurable set with the property that the Gabor system associated with the same parameters a,b and the window g=χE, forms a tight frame for L2(S).  相似文献   

10.
We describe an algorithm for constructing a Lagrange interpolation pair based on C1 cubic splines defined on tetrahedral partitions. In particular, given a set of points , we construct a set P containing and a spline space based on a tetrahedral partition whose set of vertices include such that interpolation at the points of P is well-defined and unique. Earlier results are extended in two ways: (1) here we allow arbitrary sets , and (2) the method provides optimal approximation order of smooth functions.  相似文献   

11.
A simply connected domain is called a slit disc if minus a finite number of closed radial slits not reaching the origin. A slit disc is called rational (rationally placed) if the lengths of all its circular arcs between neighboring slits (the arguments of the slits) are rational multiples of 2π. The conformal mapping of onto , (0)=0, (0)>0, extends to a continuous function on mapping it onto . A finite union E of closed non-intersecting arcs ek on is called rational if for every k, νE(ek) being the harmonic measures of ek at for the domain . A compact E is rational if and only if there is a rational slit disc such that . A compact E essentially supports a measure with periodic Verblunsky parameters if and only if for a rationally placed . For any tuple (α1,…,αg+1) of positive numbers with ∑kαk=1 there is a finite family of closed non-intersecting arcs ek on such that νE(ek)=αk. For any set and any >0 there is a rationally placed compact such that the Lebesgue measure |EE*| of the symmetric difference EE* is smaller than .  相似文献   

12.
Let mp be the minimum of the product under the conditions that and . In our previous paper [J. Kaneko, On an extremal problem of Selberg, J. Approx. Theory 142 (2006) 129–137], we showed that the following estimates hold. provided p255. In this note, we prove that the limit of as p→∞ exists and is expressed by the (unique) solution of some simultaneous transcendental equations. By using this expression we obtain numerically.  相似文献   

13.
We study the Kolmogorov n-widths and the linear n-widths of weighted Sobolev classes on the unit ball Bd in Lq,μ, where Lq,μ, 1≤q, denotes the weighted Lq space of functions on Bd with respect to weight . Optimal asymptotic orders of and as n are obtained for all 1≤p,q and μ≥0.  相似文献   

14.
We prove that the quantum double of the quasi-Hopf algebra of dimension attached in [P. Etingof, S. Gelaki, On radically graded finite-dimensional quasi-Hopf algebras, Mosc. Math. J. 5 (2) (2005) 371–378] to a simple complex Lie algebra and a primitive root of unity q of order n2 is equivalent to Lusztig's small quantum group (under some conditions on n). We also give a conceptual construction of using the notion of de-equivariantization of tensor categories.  相似文献   

15.
Let be an ideal of subsets of a metric space X,d. This paper considers a strengthening of the notion of uniform continuity of a function restricted to members of which reduces to ordinary continuity when consists of the finite subsets of X and agrees with uniform continuity on members of when is either the power set of X or the family of compact subsets of X. The paper also presents new function space topologies that are well suited to this strengthening. As a consequence of the general theory, we display necessary and sufficient conditions for continuity of the pointwise limit of a net of continuous functions.  相似文献   

16.
Dan Yasaki   《Journal of Algebra》2009,322(11):4132
Let ζ be a primitive fifth root of unity and let F be the cyclotomic field . Let be the ring of integers. We compute the Voronoï polyhedron of binary Hermitian forms over F and classify -conjugacy classes of perfect forms. The combinatorial data of this polyhedron can be used to compute the cohomology of the arithmetic group and Hecke eigenforms.  相似文献   

17.
Wolfgang Rump   《Journal of Algebra》2007,310(2):648-670
We associate a positive real number to any vector space K-category over a field K. Generalizing a result of Nazarova and Roiter, we show that a schurian vector space K-category is representation-finite if and only if is finite and . Such vector space categories are quasilinear, i.e. its indecomposables are simple modules over their endomorphism ring. Recently, Nazarova and Roiter introduced the concept of -faithful poset in order to clarify the structure of critical posets. Their conjecture on the precise form of -faithful posets was established by Zeldich. We generalize these results and characterize -faithful quasilinear vector space K-categories in terms of a class of hereditary algebras Hρ(D) parametrized by a skew-field D and a rational number ρ1.  相似文献   

18.
Let λ be a positive number, and let be a fixed Riesz-basis sequence, namely, (xj) is strictly increasing, and the set of functions is a Riesz basis (i.e., unconditional basis) for L2[−π,π]. Given a function whose Fourier transform is zero almost everywhere outside the interval [−π,π], there is a unique sequence in , depending on λ and f, such that the function
is continuous and square integrable on (−,), and satisfies the interpolatory conditions Iλ(f)(xj)=f(xj), . It is shown that Iλ(f)converges to f in , and also uniformly on , as λ→0+. In addition, the fundamental functions for the univariate interpolation process are defined, and some of their basic properties, including their exponential decay for large argument, are established. It is further shown that the associated interpolation operators are bounded on for every p[1,].  相似文献   

19.
Let p be a trigonometric polynomial, non-negative on the unit circle . We say that a measure σ on belongs to the polynomial Szegő class, if , σs is singular, and
For the associated orthogonal polynomials {n}, we obtain pointwise asymptotics inside the unit disc . Then we show that these asymptotics hold in L2-sense on the unit circle. As a corollary, we get an existence of certain modified wave operators.  相似文献   

20.
As a natural generalization of fuzzy metric spaces due to George and Veeramani [George A, Veeramani P. On some result in fuzzy metric space. Fuzzy Sets Syst 1994;64:395–9], the present author defined the notion of -fuzzy metric spaces. In this paper we prove some known results of metric spaces including Uniform continuity theorem and Ascoli–Arzela theorem for -fuzzy metric spaces. We also prove that every -fuzzy metric space has a countably locally finite basis and use this result to conclude that every -fuzzy metric space is metrizable.  相似文献   

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