scholarly journals A spectral Paley-Wiener theorem for the Heisenberg group and a support theorem for the twisted spherical means on \mathbb{C}^n

2006 ◽  
Vol 56 (2) ◽  
pp. 459-473 ◽  
Author(s):  
E. K. Narayanan ◽  
S. Thangavelu
Keyword(s):  
Heisenberg Group ◽  
Spherical Means ◽  
Support Theorem ◽  
Wiener Theorem

A Paley-Wiener Theorem for the Spherical Transform Associated with the Generalized Gelfand Pair $(U(p,q),H_{n})$, $p+q=n$

2016 ◽  
Vol 119 (2) ◽  
pp. 249
Author(s):  
Silvina Campos
Keyword(s):  
Heisenberg Group ◽  
Holomorphic Functions ◽  
Real Variable ◽  
Gelfand Pair ◽  
Wiener Theorem ◽  
Spherical Transforms

In this work we prove a Paley-Wiener theorem for the spherical transform associated to the generalized Gelfand pair $(H_n\ltimes U(p,q),H_n)$, where $H_n$ is the $2n+1$-dimensional Heisenberg group. In particular, by using the identification of the spectrum of $(U(p,q),H_n)$ with a subset $\Sigma$ of $\mathbb{R}^2$, we prove that the restrictions of the spherical transforms of functions in $C_{0}^{\infty}(H_n)$ to appropriated subsets of $\Sigma$, can be extended to holomorphic functions on $\mathbb{C}^2$. Also, we obtain a real variable characterizations of such transforms.

Injectivity sets for spherical means on the Heisenberg group

1999 ◽  
Vol 5 (4) ◽  
pp. 363-372 ◽  
Author(s):  
Mark L. Agranovsky ◽  
Rama Rawat
Keyword(s):  
Heisenberg Group ◽  
Spherical Means

scholarly journals Paley_ Wiener Theorems for The Fourier Transform depending on the Heisenberg group: مبرهنات بالي _ وينر لتحويل فورييه اعتماداً على زمرة هايزنبرغ

2020 ◽  
Vol 4 (3) ◽  
Author(s):  
Soha Ali Salamah
Keyword(s):  
Fourier Transform ◽  
Representation Theory ◽  
Heisenberg Group ◽  
Fourier Transforms ◽  
Mathematical Concepts ◽  
Weyl Transform ◽  
Wiener Theorem ◽  
Group Fourier Transform ◽  
The Fourier Transform ◽  
Compactly Supported Functions

  In this paper, we talk about Heisenberg group, the most known example from the lie groups. After that, we discuss the representation theory of this group and the relationship between the representation theory of the Heisenberg group and the position and momentum operators and momentum operators relationship between the representation theory of the Heisenberg group and the position and momentum that shows how we will make the connection between the Heisenberg group and physics. we have considered only the Schrodinger picture. That is, all the representations we considered are realized in the Hilbert space . we define the group Fourier transform on the Heisenberg group as an operator-valued function, and other facts and properties. In our research, we depended on new formulas for some mathematical concepts such as Fourier Transform and Weyl transform. The main aim of our research is to introduce the Paley_ Wiener theorem for the Fourier transform on the Heisenberg group. We will show that the classical Paley_ Wiener theorem for the Euclidean Fourier transform characterizes compactly supported functions in terms of the behaviour of their Fourier transforms and Weyl transform. And we are interested in establishing results for the group Fourier transform and the Weyl transform.

scholarly journals Complete transformation of Radon-Kipriyanov. Some properties

2019 ◽  
Vol 489 (2) ◽  
pp. 125-130
Author(s):  
L. N. Lyakhov ◽  
M. G. Lapshina ◽  
S. A. Roshchupkin
Keyword(s):  
Fourier Transform ◽  
Differential Operator ◽  
Differential Operators ◽  
Support Theorem ◽  
Singular Differential Operator ◽  
Wiener Theorem ◽  
Bessel Transform ◽  
Bessel Transforms ◽  
The Fourier Transform ◽  
Complete Transformation

The even Radon-Kipriyanov transform (Kg-transform) is suitable for investigating problems with the Bessel singular differential operator Bi = 2i2+iii,i 0. In this paper, we introduce the odd Radon-Kipriyanov transform and complete Radon-Kipriyanov transform to investigation more general equations containing odd B‑derivativesiBik, k = 0, 1, 2, ... (in particular, gradients of functions). Formulas of K-transforms of singular differential operators are given. Based on the Bessel transforms introduced by B. M. Levitan and the odd Bessel transform introduced by I. A. Kipriyanov and V. V. Katrakhov, a connection was obtained between the complete Radon-Kipriyanov transform with the Fourier transform and the mixed Fourier-Levitan-Kipriyanov-Katrakhov transform. An analogue of Helgasons support theorem and an analogue of the Paley-Wiener theorem are presented.

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