共查询到20条相似文献,搜索用时 46 毫秒
1.
In an attempt to study the scope of a theorem due to Pati, the authors have established that φ(t) logK|t∈B
u
V in (0,π)⟹ΣA
n
(x) is |C, 0,β| forβ>1, at the pointt = x. 相似文献
2.
Josef Obermaier 《Journal of Approximation Theory》2003,125(2):303-312
Let
be compact with #S=∞ and let C(S) be the set of all real continuous functions on S. We ask for an algebraic polynomial sequence (Pn)n=0∞ with deg Pn=n such that every fC(S) has a unique representation f=∑i=0∞ αiPi and call such a basis Faber basis. In the special case of
, 0<q<1, we prove the existence of such a basis. A special orthonormal Faber basis is given by the so-called little q-Legendre polynomials. Moreover, these polynomials state an example with A(Sq)≠U(Sq)=C(Sq), where A(Sq) is the so-called Wiener algebra and U(Sq) is the set of all fC(Sq) which are uniquely represented by its Fourier series. 相似文献
3.
Michel Talagrand 《Journal of Theoretical Probability》1992,5(2):327-331
Consider a (complex) Banach spaceX, such thatX CO, and vectors(X
i
)
i
ofX. Consider an independent standard normal sequence(g
i
)
i
. Then if anX-valued random Fourier series |k|
n
e
ikt
g
k
x
k
satisfies
相似文献
4.
Boniface Nkemzi 《Mathematical Methods in the Applied Sciences》2005,28(1):29-41
Partial Fourier series expansion is applied to the Dirichlet problem for the Lamé equations in axisymmetric domains ??3 with conical points on the rotation axis. This leads to dimension reduction of the three‐dimensional boundary value problem resulting to an infinite sequence of two‐dimensional boundary value problems on the plane meridian domain Ωa?? of with solutions u n(n=0,1,2,…) being the Fourier coefficients of the solution û of the 3D BVP. The asymptotic behaviour of the Fourier coefficients u n (n=0,1,2,…) near the angular points of the meridian domain Ωa is fully described by singular vector‐functions which are related to the zeros αn of some transcendental equations involving Legendre functions of the first kind. Equations which determine the values of αn are given and a numerical algorithm for the computation of αn is proposed with some plots of values obtained presented. The singular vector functions for the solution of the 3D BVP is obtained by Fourier synthesis. Copyright © 2004 John Wiley & Sons, Ltd 相似文献
5.
Wlodzimier Greblicki Miroslaw Pawlak 《Annals of the Institute of Statistical Mathematics》1985,37(1):443-454
Summary In the paper we estimate a regressionm(x)=E {Y|X=x} from a sequence of independent observations (X
1,Y
1),…, (X
n, Yn) of a pair (X, Y) of random variables. We examine an estimate of a type
, whereN depends onn andϕ
N is Dirichlet kernel and the kernel associated with the hermite series. Assuming, that E|Y|<∞ and |Y|≦γ≦∞, we give condition for
to converge tom(x) at almost allx, provided thatX has a density. if the regression hass derivatives, then
converges tom(x) as rapidly asO(nC−(2s−1)/4s) in probability andO(n
−(2s−1)/4s logn) almost completely. 相似文献
6.
Let μ be a finite positive Borel measure supported in [−1,1] and introduce the discrete Sobolev-type inner product
7.
In this paper we establish the following results, which are the multidimensional generalizations of well-known theorems:
8.
Hiro-O Kitax 《Mathematische Nachrichten》1998,193(1):57-74
Let S* (f be the majorant function of the partial sums of the trigonometric Fourier series of f. In this paper we consider the Orlicz space Lπ and give a generalization of Soria's result [S1]. Let π (t) be a concave function with some nice properties and . If there exists a positive constant a0 < 1 such that then we have . 相似文献
9.
A. K. Sahoo 《Proceedings Mathematical Sciences》2003,113(3):223-241
The object of the present paper is to study the absoluteN
qα-summability of rth derived conjugate series generalizing a known result. 相似文献
10.
scar Ciaurri 《Journal of Approximation Theory》2004,126(2):126-140
Let Jμ denote the Bessel function of order μ. The systemwith n=0,1,…,α>−1, and where ps denotes the sth positive zero of Jα(ax), is orthonormal in
. In this paper, we study the mean convergence of the Fourier series with respect to this system. Also, we describe the space in which the span of the system is dense. 相似文献
11.
Takumi Noda 《The Ramanujan Journal》2007,14(3):405-410
We give a sufficient condition of bounded growth for the non-holomorphic Eisenstein series on SL
2(ℤ). The C
∞-automorphic forms of bounded growth are introduced by Sturm (Duke Math. J. 48(2), 327–350, 1981) in the study of automorphic L-functions. We also give a Laplace-Mellin transform of the Fourier coefficients of the Eisenstein series. The transformation
constructs a projection of the Eisenstein series to the space of holomorphic cusp forms.
相似文献
12.
Jianqiang Zhao 《数学学报(英文版)》2008,24(10):1593-1616
In this paper, we shall define the renormalization of the multiple q-zeta values (MqZV) which are special values of multiple q-zeta functions ζq (s1,..., Sd) when the arguments are all positive integers or all non-positive integers. This generalizes the work of Guo and Zhang (Renormalization of Multiple Zeta Values, arxiv: math/0606076v3). We show that our renormalization process produces the same values if the MqZVs are well-defined originally and that these renormalizations of MqZV satisfy the q-stuffle relations if we use shifted-renormalizations for all divergent ζq(S1,..., sd) (i.e., s1 ≤ 1). Moreover, when q ↑ 1 our renormalizations agree with those of Guo and Zhang. 相似文献
13.
I. I. Sharapudinov 《Mathematical Notes》2000,67(3):389-397
Let
N+2m
={−m, −m+1, …, −1, 0, 1, …,N−1,N, …,N−1+m}. The present paper is devoted to the approximation of discrete functions of the formf :
N+2m
→ ℝ by algebraic polynomials on the grid Ω
N
={0, 1, …,N−1}. On the basis of two systems of Chebyshev polynomials orthogonal on the sets Ω
N+m
and Ω
N
, respectively, we construct a linear operatorY
n+2m, N
=Y
n+2m, N
(f), acting in the space of discrete functions as an algebraic polynomial of degree at mostn+2m for which the following estimate holds (x ε Ω
N
):
14.
E. D. Nursultanov 《Mathematical Notes》1998,63(2):205-214
In this paper we prove theorems on multiplicators of Fourier series inL
p, where the conditions depend on a parameterp. An example illustrating the importance of these conditions is constructed.
Translated fromMatematicheskie Zametki, Vol. 63, No. 2, pp. 235–247, February, 1998. 相似文献
15.
Suppose we have a Dirichlet series L(s) =
n = 1
a
n
n
–s such that it, and its twists by Dirichlet characters have analytic continuation and a functional equation of a specific kind. Suppose also that the root numbers of the twists are equidistributed on the unit circle. The purpose of this note is to get an estimate for the quantity
for a prime modulus p.We use a modification of the method of Chandrasekharan and Narasimhan and we use in an essential way a Rankin-Selberg type estimate for the average of |a
n|2. 相似文献
16.
It is proved that the complex double Fourier series of an integrable functionf(x, y) with coefficients cjk satisfying certain conditions, will converge in L1-norm. The conditions used here are the combinations of Tauberian condition of Hardy-Karamata kind and its limiting case.
This paper extends the result of Bray [1] to complex double Fourier series.
An erratum to this article is available at . 相似文献
17.
George E. Andrews 《The Ramanujan Journal》2007,13(1-3):311-318
In a letter dated March 3, 1971, L. Carlitz defined a sequence of polynomials, Φ
n
(a,b; x, y; z), generalizing the Al-Salam & Carlitz polynomials, but closely related thereto. He concluded the letter by stating: “It would
be of interest to find properties of Φ
n
(a, b; x, y; z) when all the parameters are free.” In this paper, we reproduce the Carlitz letter and show how a study of Carlitz’s polynomials
leads to a clearer understanding of the general 3Φ2 (a, b, c; d; e; q, z).
Dedicated to my friend, Richard Askey.
2000 Mathematics Subject Classification Primary—33D20.
G. E. Andrews: Partially supported by National Science Foundation Grant DMS 0200047. 相似文献
18.
A. G. Areshkina 《Mathematical Notes》1998,64(2):154-158
On a measurable space (T, , ) we choose an additive measure: Z (Z is a Banach space) with the following property: for alle , we have
; this measure defines an indefinite integral over the measure onL
2
(T, ,). We prove that if {
n
(t)}
n
=1/
is an orthonormal basis inL
2 and
n
(e)=e
n
(t) d, then any additive measure: Z whose Radon-Nikodým derivatived/d belongs toL
2 is uniquely expandable in a series(e)=
n
=1/
n
n(e) that converges to(e) uniformly with respect toe can be differentiated term-by-term, and satisfies
n
=1/
n
/2
<. In the caseL
2[0,2],Z=, the Fourier series of a 2-periodic absolutely continuous functionF(t) such thatF'(t) L
2[0, 2] is superuniformly convergent toF(t).Translated fromMatematicheskie Zametki, Vol. 64, No. 2, pp. 180–184, August, 1998. 相似文献
19.
M. I. D’yachenko 《Russian Mathematics (Iz VUZ)》2008,52(5):32-40
Earlier we introduced a continuous scale of monotony for sequences (classes M α, α ≥ 0), where, for example, M 0 is the set of all nonnegative vanishing sequences, M 1 is the class of all nonincreasing sequences, tending to zero, etc. In addition, we extended several results obtained for trigonometric series with monotone convex coefficients onto more general classes. The main result of this paper is a generalization of the well-known Hardy—Littlewood theorem for trigonometric series, whose coefficients belong to classes M α, where α ∈ ( $ \tfrac{1} {2}
20.
In this work the Dirichlet series
associated with real strongly q-multiplicative functions f(n) are studied. We will confine ourselves to the case
i=0
q–1
f(i) = 0. It is known that in this case the function
f
(s) has an analytic continuation to the whole complex plane as an entire function with trivial zeros on the negative real line. The real function
f
(t) satisfying the integral equation with delayed argument
for some nonzero real
f
naturally appears in the representation of the function
f
(s). In this article we find some asymptotic properties of the function
f
(s), prove that
f
(s) is an entire function of order 2, and also prove that in the region
the function
f
(s) has only trivial zeros which are simple. 相似文献
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