共查询到20条相似文献,搜索用时 62 毫秒
1.
In this paper, characterizations for lim
n(R
n
(f)/(n
–1)=0 inH
and for lim
n(n
r+
R
n
(f)=0 inW
r Lip ,r1, are given, while, forZ, a generalization to a related result of Newman is established.Communicated by Ronald A. DeVore. 相似文献
2.
Juan L. Varona 《Constructive Approximation》1994,10(1):65-75
LetJ
denote the Bessel function of order . For >–1, the system x–/2–1/2J+2n+1(x1/2, n=0, 1, 2,..., is orthogonal onL
2((0, ),x
dx). In this paper we study the mean convergence of Fourier series with respect to this system for functions whose Hankel transform is supported on [0, 1].Communicated by Mourad Ismail. 相似文献
3.
N. M. Temme 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1990,41(1):114-126
We give a brief summary of recent results concerning the asymptotic behaviour of the Laguerre polynomialsL
n
()
(x). First we summarize the results of a paper of Frenzen and Wong in whichn and >–1 is fixed. Two different expansions are needed in that case, one with aJ-Bessel function and one with an Airy function as main approximant. Second, three other forms are given in which is not necessarily fixed. These results follow from papers of Dunster and Olver, who considered the expansion of Whittaker functions. Again Bessel and Airy functions are used, and in another form the comparison function is a Hermite polynomial. A numerical verification of the new expansion in terms of the Hermite polynomial is given by comparing the zeros of the approximant with the related zeros of the Laguerre polynomial. 相似文献
4.
Kevin O'Bryant 《Journal of Algebraic Combinatorics》2004,19(1):91-115
A Sturmian word is a map W :
{0,1} for which the set of {0, 1}-vectors F
n(W) {(W(i), W(i + 1),...,W(i + n – 1))
T
: i
} has cardinality exactly n + 1 for each positive integer n. Our main result is that the volume of the simplex whose n + 1 vertices are the n + 1 points in F
n(W) does not depend on W. Our proof of this motivates studying algebraic properties of the permutation ,n
(where is any irrational and n is any positive integer) that orders the fractional parts {}, {2},...,{n}, i.e., 0 < {,n
(1)} < {,n
(2)} < ··· < {,n
(n)} < 1. We give a formula for the sign of ,n
, and prove that for every irrational there are infinitely many n such that the order of ,n
(as an element of the symmetric group S
n) is less than n. 相似文献
5.
Walter Van Assche 《Constructive Approximation》1989,5(1):329-345
The asymptotic behavior of thenth root of the leading coefficient of orthogonal polynomials on (–,) and the distribution of their zeros is studied for nonsymmetric weights that behave like exp(–2B|x|) whenx>0 and exp(–2Ax
) whenx<0,>0,>AB. These results generalize previous investigations of Rakhmanov and Mhaskar and Saff who handle the symmetric caseA=B.Communicated by Paul Nevai. 相似文献
6.
Let be a positive number, and letE
n,n
(x
;[0,1]) denote the error of best uniform rational approximation from
n,n
tox
on the interval [0,1]. We rigorously determined the numbers {E
n,n
(x
;[0,1])}
n
=1/30
for six values of in the interval (0, 1), where these numbers were calculated with a precision of at least 200 significant digits. For each of these six values of , Richardson's extrapolation was applied to the products
to obtain estimates of
相似文献
7.
Two compact algorithms are developed for solving systems of linear equationsV x=b andV
T
a=f, whereV=V(
0,
1, ...,
n
) is a confluent Vandermonde matrix of Hermite type. The solution is obtained by one forward and one backward vector recursion, starting with the right hand side. The total amount of storage is only 2n. The number of arithmetic operations needed isO(n
2) and compares favourably with other proposed methods. 相似文献
8.
9.
Thomas Stehling 《Combinatorica》1992,12(4):475-479
We consider the numberN
A
(r) of subgroups of orderp
r
ofA, whereA is a finite Abelianp-group of type =1,2,...,
l
()), i.e. the direct sum of cyclic groups of order ii. Formulas for computingN
A
(r) are well known. Here we derive a recurrence relation forN
A
(r), which enables us to prove a conjecture of P. E. Dyubyuk about congruences betweenN
A
(r) and the Gaussian binomial coefficient
. 相似文献
10.
M. Rosenblatt 《Probability Theory and Related Fields》1979,49(2):125-132
Summary Limit theorems with a non-Gaussian limiting distribution have been obtained, under appropriate conditions for partial sums of instantaneous nonlinear functions of stationary Gaussian sequences with long range dependence by a number of people. The normalization has typically been n
, with 1/2<<1 where n is the sample size. Here examples of limit theorems are given for quadratic functions with long range memory (not instantaneous) with a normalization n
, 0<<1/2.Research supported in part by the Office of Naval Research 相似文献
11.
Let F(x) = xn+1 xn-1+2 xn-2+ ··· +n be a polynomial with complex coefficients, and suppose we are given a partition (1,...,r) of n. It is a classical problem to determine explicit algebraic conditions on the i so that F may have roots with multiplicities 1,...,r. We give an invariant theoretic solution to this problem, to wit, we exhibit a set of covariants of F whose vanishing is a necessary and sufficient condition. The construction of such covariants is combinatorial, and involves associating a set of graphs on n vertices (called decisive graphs) to each .Received: 28 September 2003 相似文献
12.
The following results are obtained: If >0, 2,
[3, 4], andf is a nondecreasing (convex) function on [–1, 1] such thatE
n
(f) n
– for any n>, then E
n
(1)
(f)Cn
– (E
n
(2)
(f)Cn
–) for n>, where C=C(), En(f) is the best uniform approximation of a continuous function by polynomials of degree (n–1), and E
n
(1)
(f) (E
n
(2)
(f)) are the best monotone and convex approximations, respectively. For =2 ( [3, 4]), this result is not true.Published in Ukrainskii Matematicheskii Zhurnal, Vol. 46, No. 9, pp. 1266–1270, September, 1994. 相似文献
13.
We investigate the uniform distribution of the sequence n
as n ranges over the natural numbers and is a fixed positive real number which is not an integer. We then apply this in conjunction with the Linnik-Vaughan method to study the uniform distribution of the sequence p
as p ranges over the prime numbers. 相似文献
14.
P. Révész 《Probability Theory and Related Fields》1992,93(1):21-37
Summary We say that the discD()R
2, of radius , located around the origin isp-covered in timeT by a Wiener processW(·) if for anyzD() there exists a 0tT such thatW(t) is a point of the disc of radiusp, located aroundz. The supremum of those 's (0) is studied for which,D() isp-covered inT. 相似文献
15.
We show that there are no entire, positive, stable solutions in
n
of the Euler equation corresponding to the singular variational integral
,>0, if+n<5.236.... Furthermore we prove a related result for smooth boundaries of least-energy |x
n+1||D
U
| in
n+1. 相似文献
16.
The necessary and sufficient conditions are found for the weight function v, which provide the boundedness and compactness of the Riemann–Liouville operator R
from L
p to
. The criteria are also established for the weight function w, which guarantee the boundedness and compactness of the Weyl operator W
from
to L
q. 相似文献
17.
We study the large-time behavior and rate of convergence to the invariant measures of the processes dX
(t)=b(X)
(t)) dt + (X
(t)) dB(t). A crucial constant appears naturally in our study. Heuristically, when the time is of the order exp( – )/2 , the transition density has a good lower bound and when the process has run for about exp( – )/2, it is very close to the invariant measure. LetL
=(2/2) – U · be a second-order differential operator on d. Under suitable conditions,L
z has the discrete spectrum
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