共查询到20条相似文献,搜索用时 102 毫秒
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
利用正规实型对称空间上热核的一个上界估计及非紧致Riemann对称空间上热核 的一个梯度估计,证明了正规实型对称空间上的Littlewood-Paley平方函数算子的弱1-1 有界性. 相似文献
11.
12.
Prediction theory and Fourier Series in several variables 总被引:7,自引:0,他引:7
13.
《Indagationes Mathematicae》2005,16(3-4):461-486
Following ideas of van Dijk and Hille we study the link which exists between maximal degenerate representations and Berezin kernels.We consider the conformal group Conf(V) of a simple real Jordan algebra V. The maximal degenerate representations πs (s ε ℂ) we shall study are induced by a character of a maximal parabolic subgroup P¯ of Conf(V). These representations πs can be realized on a space Is of smooth functions on V. There is an invariant bilinear form ℬs on the space Is. The problem we consider is to diagonalize this bilinear form ℬs, with respect to the action of a symmetric subgroup G of the conformal group Conf(V). This bilinear form can be written as an integral involving the Berezin kernel Bv an invariant kernel on the Riemannian symmetric space G/K, which is a Makarevich symmetric space in the sense of Bertram. Then we can use results by van Dijk and Pevzner who computed the spherical Fourier transform of Bv. From these, one deduces that the Berezin kernel satisfies a remarkable Bernstein identity: D(ν)Bν=b(ν)Bν+1, where D(ν) is an invariant differential operator on G/K and b(ν) is a polynomial. By using this identity we compute a Hua type integral which gives the normalizing factor for an intertwining operator from I−s to Is. Furthermore, we obtain the diagonalization of the invariant bilinear form with respect to the action of the maximal compact group U of the conformal group Conf(V). 相似文献
14.
Tom K?rner 《Acta Appl Math》1989,15(3):302-303
Book Reviews
Fourier analysisT. W. Körner: Cambridge University Press, Cambridge, 1988, 591 pp. $95 相似文献15.
16.
Chi-Wai Leung 《Journal of Functional Analysis》2006,238(2):636-648
Let Ω be a measurable subset of a compact group G of positive Haar measure. Let be a non-negative function defined on the dual space and let L2(μ) be the corresponding Hilbert space which consists of elements (ξπ)π∈suppμ satisfying , where ξπ is a linear operator on the representation space of π, and is equipped with the inner product: . We show that the Fourier transform gives an isometric isomorphism from L2(Ω) onto L2(μ) if and only if the restrictions to Ω of all matrix coordinate functions , π∈suppμ, constitute an orthonormal basis for L2(Ω). Finally compact connected Lie groups case is studied. 相似文献
17.
The paper deals with the problems of divergence of the series from absolute values of the Fourier coefficients of functions in several variables. It is proved that as the dimension of the space increases, the absolute convergence of Fourier series with respect to any complete orthnormal system (ONS) of functions with continuous partial derivatives becomes worse. For instance, for any ? ∈ (0, 2) there exists a function in variables $k > \frac{{2(2 - \varepsilon )}} {\varepsilon }$ having all the continuous partial derivatives, however the series of absolute values of its coefficients with respect to any complete orthnormal system diverges in power 2 ? ?. 相似文献
18.
Leonardo Colzani 《Transactions of the American Mathematical Society》2006,358(12):5501-5521
In the first part of the paper we establish the pointwise convergence as for convolution operators under the assumptions that has integrable derivatives up to an order and that with . We also estimate the Hausdorff dimension of the set where divergence may occur. In particular, when the kernel is the Fourier transform of a bounded set in the plane, we recover a two-dimensional analog of the Dirichlet theorem on the convergence of Fourier series of functions with bounded variation. In the second part of the paper we prove an equiconvergence result between Fourier integrals on euclidean spaces and expansions in eigenfunctions of elliptic operators on manifolds, which allows us to transfer some of the results proved for Fourier integrals to eigenfunction expansions. Finally, we present some examples of different behaviors between Fourier integrals, Fourier series and spherical harmonic expansions.
19.
Shigehiko Kuratsubo 《Proceedings of the American Mathematical Society》1999,127(10):2987-2994
We prove the pointwise convergence of the Fourier series for radial functions in several variables, which in the case is the Dirichlet-Jordan theorem itself. In our proof the method for the case of the indicator function of the ball is very useful.
20.
Jitka Poměnková 《Applications of Mathematics》2008,53(4):305-317
Kernel smoothers belong to the most popular nonparametric functional estimates used for describing data structure. They can
be applied to the fix design regression model as well as to the random design regression model. The main idea of this paper
is to present a construction of the optimum kernel and optimum boundary kernel by means of the Gegenbauer and Legendre polynomials.
This work is part of the research project “The Czech Economy in the Process of Integration and Globalization, and the Development
of Agricultural Sector and the Sector of Service under the New Conditions of the Integrated European Market”. 相似文献