共查询到20条相似文献,搜索用时 0 毫秒
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William O. Bray 《Monatshefte für Mathematik》1993,116(1):1-11
The Fourier inversion formula in polar form is \(f(x) = \int_0^\infty {P_\lambda } f(x)d\lambda \) for suitable functionsf on ? n , whereP λ f(x) is given by convolution off with a multiple of the usual spherical function associated with the Euclidean motion group. In this form, Fourier inversion is essentially a statement of the spectral theorem for the Laplacian and the key question is: how are the properties off andP λ f related? This paper provides a Paley-Wiener theorem within this avenue of thought generalizing a result due to Strichartz and provides a spectral reformulation of a Paley-Wiener theorem for the Fourier transform due to Helgason. As an application we prove support theorems for certain functions of the Laplacian. 相似文献
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The Fourier coefficients of a smooth K-invariant function on a compact symmetric space M=U/K are given by integration of the function against the spherical functions. For functions with support in a neighborhood of the origin, we describe the size of the support by means of the exponential type of a holomorphic extension of the Fourier coefficients. 相似文献
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Duren Peter; Gallardo-Gutierrez Eva A.; Montes-Rodriguez Alfonso 《Bulletin London Mathematical Society》2007,39(3):459-466
An analogue of the PaleyWiener theorem is developed forweighted Bergman spaces of analytic functions in the upper half-plane.The result is applied to show that the invariant subspaces ofthe shift operator on the standard Bergman space of the unitdisk can be identified with those of a convolution Volterraoperator on the space L2(+, (1/t)dt). 相似文献
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Swanhild Bernstein 《Advances in Applied Clifford Algebras》1998,8(1):31-46
Using the properties of the monogenic extension of the Fourier transform, we state a Paley-Wiener-type theorem for monogenic
functions. Based on an multiplier algebra related to boundary values of monogenic functions we consider integral equations
of Wiener-Hopf-typeK±u
±=f on ℝ
n
, whereK ∈S′ andu
± are boundary values of monogenic functions in ℝ+
n+1 and ℝ_
n+1 respectivly. 相似文献
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Translated from Matematicheskie Zametki, Vol. 48, No. 5, pp. 80–87, November, 1990. 相似文献
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The classical Paley-Wiener theorem for functions in L
dx
2
relates the growth of the Fourier transform over the complex plane to the support of the function. In this work we obtain
Paley-Wiener type theorems where the Fourier transform is replaced by transforms associated with self-adjoint operators on
L
dμ
2
, with simple spectrum, where dμ is a Lebesgue-Stieltjes measure. This is achieved via the use of support preserving transmutations.
Communicated by Paul L. Butzer 相似文献
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S. V. Sharin 《Journal of Mathematical Sciences》1999,96(2):2985-2987
LetD+ be the space of Schwartz distributions with support on the closed positive half-line [0, +). We give a generalization of the Paley-Wiener theorem to the case of the distributions inD+.Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 4, 1997, pp. 54–57. 相似文献
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Nils Byrial Andersen Gestur Ó lafsson 《Proceedings of the American Mathematical Society》2001,129(1):173-179
We formulate and prove a topological Paley-Wiener theorem for the normalized spherical Laplace transform defined on the rank 1 causal symmetric spaces , for .
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We introduce a global wave front set suitable for the analysis of tempered ultradistributions of quasi-analytic Gelfand–Shilov type. We study the transformation properties of the wave front set and use them to give microlocal existence results for pullbacks and products. We further study quasi-analytic microlocality for classes of localization and ultradifferential operators, and prove microellipticity for differential operators with polynomial coefficients. 相似文献
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The Paley-Wiener theorem in the non-commutative and non-associative octonion analytic function space is proved.
This work was supported by the National Basic Research Program of China (Grant No. 1999075105), the National Natural Science
Foundation of China (Grant No. 10471002) and Research Foundation for Doctoral Programm (Grant No. 20050574002) 相似文献
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Ioana Cioranescu 《Mathematische Zeitschrift》1990,204(1):391-400
Supported by DAAD, West Germany 相似文献
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Jiri Dadok 《Journal of Functional Analysis》1979,31(3):341-354
We study Fourier transforms of distributions on a symmetric space X. Eguchi et al. [1] characterized the image of ′(X)-distributions of compact support under the Fourier transform. We give a simpler proof of Eguchi's result and characterize the size of the singular support for the K-finite members of E′(X). We apply this Paley-Wiener type theorem to invariant differential equations on X. 相似文献