共查询到20条相似文献,搜索用时 15 毫秒
1.
Associated with the Dirac operator and partial derivatives, this paper establishes some real Paley-Wiener type theorems to characterize the Clifford-valued functions whose Clifford Fourier transform (CFT) has compact support. Based on the Riemann-Lebesgue theorem for the CFT, the Boas theorem is provided to describe the CFT of Clifford-valued functions that vanish on a neighborhood of the origin. 相似文献
2.
R. Radha 《Journal of Mathematical Analysis and Applications》2009,354(2):564-574
The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on Rn and Cn under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved. 相似文献
3.
Hugo Rodríguez-Ordez 《Expositiones Mathematicae》2007,25(4):355-361
This paper is a revision of a portion of the author's doctoral dissertation submitted to the University of Oregon. Using elementary concepts of K-theory, the Brouwer degree of the power map in the octonions is computed. Later, a proof of a weaker version of the fundamental theorem of algebra for polynomials with coefficients in the octonions is given. As a partial complement, a lower bound to the number of solutions of a homogeneous monomial equation over the octonions is obtained. 相似文献
4.
Young Min Han 《Journal of Mathematical Analysis and Applications》2010,370(2):538-542
In this note we consider Weyl's theorem and Browder's theorem in several variables. The main result is as follows. Let T be a doubly commuting n-tuple of hyponormal operators acting on a complex Hilbert space. If T has the quasitriangular property, i.e., the dimension of the left cohomology for the Koszul complex Λ(T−λ) is greater than or equal to the dimension of the right cohomology for Λ(T−λ) for all λ∈Cn, then ‘Weyl's theorem’ holds for T, i.e., the complement in the Taylor spectrum of the Taylor Weyl spectrum coincides with the isolated joint eigenvalues of finite multiplicity. 相似文献
5.
We show that the remainder of the Taylor expansion for a holomorphic function can be written down in Lagrange form, provided that the argument of the function is sufficiently close to the interpolation point. Moreover, the value of the derivative in the remainder can be taken in the intersection of the disk whose diameter joins the interpolation point and the argument of the function and an arbitrary small angle whose bisectrix is the ray from the interpolation point through the argument of the function. 相似文献
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7.
Fractional cosine transform (FRCT) and fractional sine transform (FRST), which are closely related to the fractional Fourier transform (FRFT), are useful mathematical and optical tool for signal processing. Many properties for these transforms are well investigated, but the convolution theorems are still to be determined. In this paper, we derive convolution theorems for the fractional cosine transform (FRCT) and fractional sine transform (FRST) based on the four novel convolution operations. And then, a potential application for these two transforms on designing multiplicative filter is presented. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献
8.
Kit-Ian KouTao Qian 《Journal of Functional Analysis》2002,189(1):227-241
We prove the Paley-Wiener Theorem in the Clifford algebra setting. As an application we derive the corresponding result for conjugate harmonic functions. 相似文献
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10.
Katusi Fukuyama Shigeru Takahashi 《Proceedings of the American Mathematical Society》1999,127(2):599-608
In this paper, the central limit theorem for lacunary trigonometric series is proved. Two gap conditions by Erdos and Takahashi are extended and unified. The criterion for the Fourier character of lacunary series is also given.
11.
In this paper,we prove a Marcinkiewicz-Zygmund type inequality for multivariate entire functions of exponential type with non-equidistant spaced sampling points. And from this result,we establish a multivariate irregular Whittaker-Kotelnikov-Shannon type sampling theorem. 相似文献
12.
Jaap Korevaar 《Proceedings of the American Mathematical Society》2006,134(4):1107-1116
The Tauberian theorem of Wiener and Ikehara provides the most direct way to the prime number theorem. Here it is shown how Newman's contour integration method can be adapted to establish the Wiener-Ikehara theorem. A simple special case suffices for the PNT. But what about the twin-prime problem?
13.
We prove that the octonionic polynomials V ■k l 1 ··· l k are independent of the associative orders ■k . This improves the octonionic Taylor type theorem. 相似文献
14.
Qiuhui Chen 《Applicable analysis》2013,92(6):903-919
This study concerns some new developments of unit analytic signals with non-linear phase. It includes ladder-shaped filter, generalized Sinc function based on non-linear Fourier atoms, generalized sampling theorem for non-bandlimited signals and the notion of multi-scale spectrum for discrete sequences. We first introduce the ladder-shaped filter and show that the impulse response of its corresponding linear time-shift invariant system is the generalized Sinc function as a product of periodic Poisson kernel and Sinc function. Secondly, we establish a Shannon-type sampling theorem based on generalized Sinc function for this type of non-bandlimited signal. We further prove that this type of signal may be holomorphically extended to strips in the complex plane containing the real axis. Finally, we introduce the notion of multi-scale spectrums for discrete sequences and develop the related fast algorithm. 相似文献
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16.
Steven G. Krantz Harold R. Parks 《Journal of Mathematical Analysis and Applications》2008,340(2):1263-1270
The classical Lagrange inversion theorem is a concrete, explicit form of the implicit function theorem for real analytic functions. An explicit construction shows that the formula is not true for all merely smooth functions. The authors modify the Lagrange formula by replacing the smooth function by its Maclaurin polynomials. The resulting modified Lagrange series is, in analogy to the Maclaurin polynomials, an approximation to the solution function accurate to o(xN) as x→0. 相似文献
17.
Roberto Camporesi 《Proceedings of the American Mathematical Society》2006,134(9):2649-2659
We prove the Paley-Wiener theorem for the spherical transform on the complex Grassmann manifolds SUSU U. This theorem characterizes the -biinvariant smooth functions on the group that are supported in the -invariant ball of radius , with less than the injectivity radius of , in terms of holomorphic extendability, exponential growth, and Weyl invariance properties of the spherical Fourier transforms , originally defined on the discrete set of highest restricted spherical weights.
18.
A modification of the Taylor expansion for the complex exponential function eix, x∈R, is proposed yielding precise moment-type estimates of the accuracy of the approximation of a Fourier transform by the first terms of its Taylor expansion. Moreover, a precise upper bound for the third moment of a probability distribution in terms of the absolute third moment is established. Based on these results, new precise bounds for Fourier–Stieltjes transforms of probability distribution functions and for their derivatives are obtained that are uniform in classes of distributions with prescribed first three moments. 相似文献
19.
We consider interpolation of discrete functions by continuous ones with restriction on the size of spectra. We discuss a sharp contrast between the cases of compact and unbounded spectra. In particular we construct ‘universal’ spectra of small measure which deliver positive solution of the interpolation problem in Bernstein spaces for every discrete sequence of knots. 相似文献
20.
We consider an extremal problem for even positive definite entire functions of exponential type with zero mean with power weight on the semiaxis. This problem is related to the multidimensional Jackson-Stechkin theorem in the space L 2(?n). 相似文献