Harmonic Analysis for Vector Fields on Hyperbolic Spaces.
H.M. Reimann, E. Badertscher (1989)
Mathematische Zeitschrift
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H.M. Reimann, E. Badertscher (1989)
Mathematische Zeitschrift
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Andersen, Nils Byrial, Unterberger, Jérémie M. (2000)
Journal of Lie Theory
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Roberto Camporesi (2016)
Colloquium Mathematicae
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We prove the Paley-Wiener theorem for the Helgason Fourier transform of smooth compactly supported 𝔳-radial functions on a Damek-Ricci space S = NA.
Francesca Astengo, Bianca Di Blasio, Fulvio Ricci (2013)
Studia Mathematica
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Let H₁ be the 3-dimensional Heisenberg group. We prove that a modified version of the spherical transform is an isomorphism between the space 𝓢ₘ(H₁) of Schwartz functions of type m and the space 𝓢(Σₘ) consisting of restrictions of Schwartz functions on ℝ² to a subset Σₘ of the Heisenberg fan with |m| of the half-lines removed. This result is then applied to study the case of general Schwartz functions on H₁.
R.J. Beerends (1987)
Mathematische Annalen
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Bellman, Richard (1978)
International Journal of Mathematics and Mathematical Sciences
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T. Godoy, L. Saal (2006)
Colloquium Mathematicae
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Let 𝓢(Hₙ) be the space of Schwartz functions on the Heisenberg group Hₙ. We define a spherical transform on 𝓢(Hₙ) associated to the action (by automorphisms) of U(p,q) on Hₙ, p + q = n. We determine its kernel and image and obtain an inversion formula analogous to the Godement-Plancherel formula.
Hikosaburo Komatsu (2010)
Banach Center Publications
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As written in L. Schwartz' book, Heaviside's theory of cables is an important source of the theory of generalized functions. The partial differential equations he discussed were the usual heat equation and the simplest hyperbolic equations of one space dimension, but he had to solve them as evolution equations in the unusual direction of the distance along which the electric signals propagate. Although he obtained explicit expressions of solutions, which were of great economical values,...
R. Bhuvaneswari, V. Karunakaran (2010)
Annales UMCS, Mathematica
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Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.
R. Bhuvaneswari, V. Karunakaran (2010)
Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica
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Function spaces of type S are introduced and investigated in the literature. They are also applied to study the Cauchy problem. In this paper we shall extend the concept of these spaces to the context of Boehmian spaces and study the Fourier transform theory on these spaces. These spaces enable us to combine the theory of Fourier transform on these function spaces as well as their dual spaces.
Karkusty, N.N. (1999)
Vladikavkazskiĭ Matematicheskiĭ Zhurnal
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Younis, M.S. (1998)
International Journal of Mathematics and Mathematical Sciences
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Shrideh K.Q. Al-Omari, Jafar F. Al-Omari (2015)
Open Mathematics
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In this paper, we establish certain spaces of generalized functions for a class of ɛs2,1 transforms. We give the definition and derive certain properties of the extended ɛs2,1 transform in a context of Boehmian spaces. The extended ɛs2,1 transform is therefore well defined, linear and consistent with the classical ɛs2,1 transforms. Certain results are also established in some detail.
Martin J. Mohlenkamp (1999)
The journal of Fourier analysis and applications [[Elektronische Ressource]]
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Per Sjölin (2002)
Rendiconti del Seminario Matematico della Università di Padova
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Carlos A. Berenstein, E.C. Tarabusi (1993)
Forum mathematicum
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Yürekli, O., Sadek, I. (1991)
International Journal of Mathematics and Mathematical Sciences
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