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21.
Zhizhiashvili studied questions associated with the approximation properties of Cesàro means of trigonometric Fourier series for functions of two variables in the spaces H. It is proved here that the corresponding estimate cannot be improved for p = 1 or p = . 相似文献
22.
We examine several interesting relationships and expressions involving Fourier-Feynman transform, convolution product and
first variation for functionals in the Fresnel class F(B) of an abstract Wiener space B. We also prove a translation theorem and Parseval's identity for the analytic Feynman integral.
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
23.
D. A. Popov 《Functional Analysis and Its Applications》2003,37(3):215-220
We consider the problem of reconstructing a function on the disk
from its integrals over curves close to straight lines, i.e., the inversion problem for the generalized Radon transform. Necessary and sufficient conditions on the range of the generalized Radon transform are obtained for functions supported in a smaller disk
under the additional condition that the curves that do not meet
coincide with the corresponding straight lines. 相似文献
24.
In this paper, the authors obtain sharp upper and lower hounds for the heat kernel associated with Jacobi transform, and get some analogues of Hardy‘s Theorem for Jacobi transform by using the sharp estimate of the heat kernel. 相似文献
25.
Let μ be a finite positive Borel measure supported in [−1,1] and introduce the discrete Sobolev-type inner productwhere the mass points ak belong to [−1,1], Mk,i0, i=0,…,Nk−1, and Mk,Nk>0. In this paper, we study the asymptotics of the Sobolev orthogonal polynomials by comparison with the orthogonal polynomials with respect to the measure μ and we prove that they have the same asymptotic behaviour. We also study the pointwise convergence of the Fourier series associated to this inner product provided that μ is the Jacobi measure. We generalize the work done by F. Marcellán and W. Van Assche where they studied the asymptotics for only one mass point in [−1,1]. The same problem with a finite number of mass points off [−1,1] was solved by G. López, F. Marcellán and W. Van Assche in a more general setting: they consider the constants Mk,i to be complex numbers. As regards the Fourier series, we continue the results achieved by F. Marcellán, B. Osilenker and I.A. Rocha for the Jacobi measure and mass points in
. 相似文献
26.
D. Barrios Rolanía G. Lpez Lagomasino E. B. Saff 《Journal of Approximation Theory》2003,124(2):263-281
Using a convergence theorem for Fourier–Padé approximants constructed from orthogonal polynomials on the unit circle, we prove an analogue of Hadamard's theorem for determining the radius of m-meromorphy of a function analytic on the unit disk and apply this to the location of poles of the reciprocal of Szeg
functions. 相似文献
27.
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
28.
Lp(Rm × Rn) boundedness is considered for the multiple Marcinkiewicz integral. Some size conditions implying the Lp(Rm × Rn) boundedness of the multiple Marcinkiewicz integral for some fixed 1 > p > ∞ are obtained. 相似文献
29.
传统的波动方程波场重建基于完全弹性介质,不能获得满意的地震资料分辨率,本基于能描述大地吸收弹性介质中地震波传播的斯托克斯波动方程.提出了一种新的多尺度粘弹性波动方程波场重建的方法,根据地震波传播核函数的物理特性,研究了一种新的物理小波,提出了小波多尺度波场重建方法。达到对吸收信息的补偿,提高地震资料的分辨率。 相似文献
30.
We discuss integral transformations of the QCD renormalization-invariant coupling (running coupling constant). Special attention is paid to the Fourier transformation, i.e., to the transition from the space–time to the energy–momentum representation. Our first conclusion is that the condition for the possibility of such a transition provides one more argument against the real existence of unphysical singularities observed in the perturbative QCD. The second conclusion relates to a way to translate some singular long-wave asymptotic behaviors to the infrared region of transferred momenta. Such a transition must be performed with the Tauberian theorem taken into account. This comment relates to the recent ALPHA collaboration results on the asymptotic behavior of the QCD effective coupling obtained by numerical lattice simulation. 相似文献