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111.
Daniel Carando Ignacio Zalduendo 《Proceedings of the American Mathematical Society》1999,127(1):241-250
We study the problem of extendibility of polynomials over Banach spaces: when can a polynomial defined over a Banach space be extended to a polynomial over any larger Banach space? To this end, we identify all spaces of polynomials as the topological duals of a space spanned by evaluations, with Hausdorff locally convex topologies. We prove that all integral polynomials over a Banach space are extendible. Finally, we study the Aron-Berner extension of integral polynomials, and give an equivalence for non-containment of .
112.
Irregular sampling, Toeplitz matrices, and the approximation of entire functions of exponential type
In many applications one seeks to recover an entire function of exponential type from its non-uniformly spaced samples. Whereas the mathematical theory usually addresses the question of when such a function in can be recovered, numerical methods operate with a finite-dimensional model. The numerical reconstruction or approximation of the original function amounts to the solution of a large linear system. We show that the solutions of a particularly efficient discrete model in which the data are fit by trigonometric polynomials converge to the solution of the original infinite-dimensional reconstruction problem. This legitimatizes the numerical computations and explains why the algorithms employed produce reasonable results. The main mathematical result is a new type of approximation theorem for entire functions of exponential type from a finite number of values. From another point of view our approach provides a new method for proving sampling theorems.
113.
We study limit distribution of partial sums SN,k(t) =
s = 1
[N t]
Ak(Xs) of Appell polynomials of the long-range dependent moving average process Xt> = i t bt - i i, where {i} is a strictly stationary and weakly dependent martingale difference sequence, and bi id - 1 (0 < d < 1/2). We show that if k(1-2 d)<1, then suitably normalized partial sums SN,k(t) converge in distribution to the kth order Hermite process. This result generalizes the corresponding results of Surgailis, and Avram and Taqqu obtained in the case of the i.i.d. sequence { i}. 相似文献
114.
We build an irreducible unitary representation of SO( ) from the usual one of SO( n ) in the space of harmonic homogeneous polynomials of degree m of
n
. We give a characterization of these new representations which extends in a natural way the finite dimensional characterization. In the particular case of SO( ), we thus get some results of Olshanskii (cf. [12]). This leads to a new proof of McKean conjecture about irreducible representations of ( infin ) (cf. [10]). 相似文献
115.
Bernard Badzioch 《K-Theory》1999,16(1):29-34
We prove that for an arbitrary endomorphism of a ring R the group K1(R[t]) splits into the direct sum of K1(R) and Ñil (r;). Moreover, for any such R and Ñil (R; ) is isomorphic to Ñil (R ; ) for some ring R with : R R – an isomorphism. 相似文献
116.
K. Farahmand 《Proceedings of the American Mathematical Society》1999,127(11):3339-3344
This paper provides asymptotic estimates for the expected number of real zeros and -level crossings of a random algebraic polynomial of the form , where are independent standard normal random variables and is a constant independent of . It is shown that these asymptotic estimates are much greater than those for algebraic polynomials of the form .
117.
After studying Gaussian type quadrature formulae with mixed boundary conditions, we suggest a fast algorithm for computing their nodes and weights. It is shown that the latter are computed in the same manner as in the theory of the classical Gauss quadrature formulae. In fact, all nodes and weights are again computed as eigenvalues and eigenvectors of a real symmetric tridiagonal matrix. Hence, we can adapt existing procedures for generating such quadrature formulae. Comparative results with various methods now in use are given. In the second part of this paper, new algorithms for spectral approximations for second-order elliptic problems are derived. The key to the efficiency of our algorithms is to find an appropriate spectral approximation by using the most accurate quadrature formula, which takes the boundary conditions into account in such a way that the resulting discrete system has a diagonal mass matrix. Hence, our algorithms can be used to introduce explicit resolutions for the time-dependent problems. This is the so-called lumped mass method. The performance of the approach is illustrated with several numerical examples in one and two space dimensions.
118.
On the distribution of the length of the longest increasing subsequence of random permutations 总被引:18,自引:0,他引:18
Jinho Baik Percy Deift Kurt Johansson 《Journal of the American Mathematical Society》1999,12(4):1119-1178
The authors consider the length, , of the longest increasing subsequence of a random permutation of numbers. The main result in this paper is a proof that the distribution function for , suitably centered and scaled, converges to the Tracy-Widom distribution of the largest eigenvalue of a random GUE matrix. The authors also prove convergence of moments. The proof is based on the steepest descent method for Riemann-Hilbert problems, introduced by Deift and Zhou in 1993 in the context of integrable systems. The applicability of the Riemann-Hilbert technique depends, in turn, on the determinantal formula of Gessel for the Poissonization of the distribution function of .
119.
Khalfa Douak 《Journal of Computational and Applied Mathematics》1996,70(2):279-295
We are dealing with the concept of d-dimensional orthogonal (abbreviated d-orthogonal) polynomials, that is to say polynomials verifying one standard recurrence relation of order d + 1. Among the d-orthogonal polynomials one singles out the natural generalizations of certain classical orthogonal polynomials. In particular, we are concerned, in the present paper, with the solution of the following problem (P): Find all polynomial sequences which are at the same time Appell polynomials and d-orthogonal. The resulting polynomials are a natural extension of the Hermite polynomials.
A sequence of these polynomials is obtained. All the elements of its (d + 1)-order recurrence are explicitly determined. A generating function, a (d + 1)-order differential equation satisfied by each polynomial and a characterization of this sequence through a vectorial functional equation are also given. Among such polynomials one singles out the d-symmetrical ones (Definition 1.7) which are the d-orthogonal polynomials analogous to the Hermite classical ones. When d = 1 (ordinary orthogonality), we meet again the classical orthogonal polynomials of Hermite. 相似文献
120.
In this paper we define a new algebra generated by the difference operators D
q and D
q-1 with two analytic functions (x) and (x). Also, we define an operator M = J
1
J
2–J
3
J
4 s.t. all q-hypergeometric orthogonal polynomials Y
n(x), x cos(), are eigenfunctions of the operator M with eigenvalues
q
[n]
q
. The choice of (x) and (x) depend on the weight function of Y
n
(x). 相似文献