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81.
Using the theory of Hankel convolution, continuous and discrete Bessel wavelet transforms are defined. Certain boundedness results and inversion formula for the continuous Bessel wavelet transform are obtained. Important properties of the discrete Bessel wavelet transform are given. 相似文献
82.
In this study, we have found upper and lower bounds for the spectral norm of Cauchy–Toeplitz and Cauchy–Hankel matrices in the forms Tn=[1/(a+(i−j)b)]ni,j=1, Hn=[1/(a+(i+j)b)]ni,j=1. 相似文献
83.
Let the real functionsK(x) andL(x) be such thatM(x)=K(x)+iL(x)=eix
g(x), whereg(x) is infinitely differentiable for all largex and is non-oscillatory at infinity. We develop an efficient automatic quadrature procedure for numerically computing the integrals
a
K(t)f(t) and
a
L(t)f(t)dt, where the functionf(t) is smooth and nonoscillatory at infinity. One such example for which we also provide numerical results is that for whichK(x)=J
(x) andL(x)=Y
(x), whereJ
(x) andY
(x) are the Bessel functions of order . The procedure involves the use of an automatic scheme for Fourier integrals and the modified W-transformation which is used for computing oscillatory infinite integrals. 相似文献
84.
85.
Skander Belhaj 《Numerical Algorithms》2008,47(1):15-34
In this paper, we consider an approximate block diagonalization algorithm of an n×n real Hankel matrix in which the successive transformation matrices are upper triangular Toeplitz matrices, and propose a
new fast approach to compute the factorization in O(n
2) operations. This method consists on using the revised Bini method (Lin et al., Theor Comp Sci 315: 511–523, 2004). To motivate our approach, we also propose an approximate factorization variant of the customary fast method based on Schur
complementation adapted to the n×n real Hankel matrix. All algorithms have been implemented in Matlab and numerical results are included to illustrate the effectiveness
of our approach. 相似文献
86.
87.
Mengkun Zhu Niall Emmart Yang Chen Charles Weems 《Mathematical Methods in the Applied Sciences》2019,42(9):3272-3288
We study the asymptotic behavior of the smallest eigenvalue, λN, of the Hankel (or moments) matrix denoted by , with respect to the weight . An asymptotic expression of the polynomials orthogonal with w(x) is established. Using this, we obtain the specific asymptotic formulas of λN in this paper. Applying a parallel numerical algorithm, we get a variety of numerical results of λN corresponding to our theoretical calculations. 相似文献
88.
In this paper, we treat an inverse problem for a radially symmetric heat equation, which arises from non-destructive evaluation by thermal imaging. The problem can also be considered as an inverse heat conduction problem. Based on a weighted energy method, we give a conditional stability estimate. A feasible regularization method is provided for numerical simulation. The reconstruction experiment is done for verifying the efficiency of the regularization method. 相似文献
89.
Guangfu Cao & Li He 《数学研究通讯:英文版》2023,39(2):254-286
In this paper, we introduce the work done on Hardy-Sobolev spaces
and Fock-Sobolev spaces and their operators and operator algebras, including the study of boundedness, compactness, Fredholm property, index theory,
spectrum and essential spectrum, norm and essential norm, Schatten-p classes,
and the $C^∗$ algebras generated by them. 相似文献
90.
若S是Dirichlet空间上有限个Toeplitz算子乘积的有限和, S为紧算子的充要条件是: 当z→∂D时, S的Berezin型变换收敛到0; 若S是Dirichlet空间上Hankel算子, S为紧算子的充要条件是: 当z→ D时, S作用在类再生核上按范数收敛到0. 相似文献