共查询到20条相似文献,搜索用时 15 毫秒
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Wolter Groenevelt 《Constructive Approximation》2009,29(1):85-127
Big q-Jacobi functions are eigenfunctions of a second-order q-difference operator L. We study L as an unbounded self-adjoint operator on an L
2-space of functions on ℝ with a discrete measure. We describe explicitly the spectral decomposition of L using an integral transform ℱ with two different big q-Jacobi functions as a kernel, and we construct the inverse of ℱ.
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The aim of this paper is to define $(p, q)$-analogue of Mittag-Leffler Function, by using $(p, q)$-Gamma function. Some transformation formulae are also derived
by using the $(p, q)$-derivative. The $(p, q)$-analogue for this function provides elegant
generalization of $q$-analogue of Mittag-Leffler function in connection with $q$-calculus.
Moreover, the $(p, q)$-Laplace Transform of the Mittag-Leffler function has been obtained. Some special cases have also been discussed. 相似文献
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该文建立了Henstock-Kurzweil 可积函数的 Laplace变换, 讨论了其基本性质及解析性质, 得到Henstock-Kurzweil可积意义下的反演公式, 并给出反例说明这一结果不能改进 相似文献
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Chokri Abdelkefi 《Mediterranean Journal of Mathematics》2012,9(3):499-513
We introduce first weighted function spaces on ${\mathbb{R}^d}$ using the Dunkl convolution that we call Besov-Dunkl spaces. We provide characterizations of these spaces by decomposition of functions. Next we obtain in the real line and in radial case on ${\mathbb{R}^d}$ weighted L p -estimates of the Dunkl transform of a function in terms of an integral modulus of continuity which gives a quantitative form of the Riemann-Lebesgue lemma. Finally, we show in both cases that the Dunkl transform of a function is in L 1 when this function belongs to a suitable Besov-Dunkl space. 相似文献
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线性正则变换是经典Fourier变换的广义形式,目前在非平稳信号的参数检测与估计方面取得了优异的应用效果,但线性正则变换理论体系还不完善.探讨了线性正则变换相关的复能量密度函数的基本概念,并详细推导研究了其基本的数学性质与特点,在上述理论的基础上,通过仿真实验来验证所得到结论的准确性.为其在实际应用中发挥更大的作用奠定了基础. 相似文献
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The spectral decomposition for an explicit second-order differential operator T is determined. The spectrum consists of a continuous part with multiplicity two, a continuous part with multiplicity one, and a finite discrete part with multiplicity one. The spectral analysis gives rise to a generalized Fourier transform with an explicit hypergeometric function as a kernel. Using Jacobi polynomials, the operator T can also be realized as a five-diagonal operator, leading to orthogonality relations for 2×2-matrix-valued polynomials. These matrix-valued polynomials can be considered as matrix-valued generalizations of Wilson polynomials. 相似文献
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New relations between the Fourier transform of a function of bounded variation and the Hilbert transform of its derivative are revealed. The main result of the paper is an asymptotic formula for the cosine Fourier transform. Such relations have previously been known only for the sine Fourier transform. For this, not only a different space is considered but also a new way of proving such theorems is applied. Interrelations of various function spaces are studied in this context. The obtained results are used for obtaining completely new results on the integrability of trigonometric series. 相似文献
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Leszek Skrzypczak 《Mathematische Nachrichten》1998,190(1):251-274
We define and investigate the Triebel - Lizorkin scale of function spaces F, with 1< p < ∞, 1< q ≤ ∞ for the Fourier-Helgason transform on symmetric Riemannian manifolds of the noncompact type. 相似文献
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通过引入双下q-型的概念,讨论了具有非正规增长的全平面收敛的Laplace-Stieltjes变换的增长性与逼近,得到了Laplace-Stieltjes变换的尾项与双下q-型,An*以及λn的关系定理,推广了罗茜,孔荫莹,Singhal与Srivastava等的结果. 相似文献
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The Clifford-Fourier Transform 总被引:2,自引:0,他引:2
Fred Brackx Nele De Schepper Frank Sommen 《Journal of Fourier Analysis and Applications》2005,11(6):669-681
A pair of Clifford-Fourier transforms is defined in the framework of Clifford analysis, as operator exponentials with a Clifford
algebra-valued kernel. It is a genuine Clifford analysis construct, which is shown to be a refinement of the classical multi-dimensional
Fourier transform. An adequate operational calculus is developed. 相似文献
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It is pointed out that difficulties can occur with the Kontorovich-Lebedevtransform when expressed in terms of Hankel functions and anew form is proposed which overcomes these difficulties. 相似文献
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该文基于Daubechies小波尺度函数变换建立了关于Laplace变换的一种反演数值方法.通过对小波尺度函数的低带通谱特性的定性与定量讨论,给出了这一反演方法所得原像函数的适用域.结果发现:其区域大小随着小波尺度函数的分辨指标(resolutionlevel)选取的升高而增大.最后,以颤振曲线、具有指数增长的复函数、和一维振动弦的初边值问题等为例,定量给出了其反演方法的数值结果.通过与相应的原像精确结果对比发现:在反演的有效区域内,其数值反演的原像几乎与精确的原像图象重合.这表明这一Laplace反演数值方法是有效和可靠的. 相似文献
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The Laplace transform of the Airy function of the first kindAi(x) is obtained conveniently as a special case of the Laplacetransform of the Macdonald function of argument 2x3/2. 相似文献