منابع مشابه
The Heisenberg Group Fourier Transform
1. Fourier transform on Rn 1 2. Fourier analysis on the Heisenberg group 2 2.1. Representations of the Heisenberg group 2 2.2. Group Fourier transform 3 2.3. Convolution and twisted convolution 5 3. Hermite and Laguerre functions 6 3.1. Hermite polynomials 6 3.2. Laguerre polynomials 9 3.3. Special Hermite functions 9 4. Group Fourier transform of radial functions on the Heisenberg group 12 Ref...
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The aim of this paper is to show that any continuous ∗-homomorphism of L(C)(with twisted convolution as multiplication) into B(L(R)) is essentially a Weyl transform. From this we deduce a similar characterisation for the group Fourier transform on the Heisenberg group, in terms of convolution.
متن کاملThe Fourier Transforms of Lipschitz Functions on the Heisenberg Group
We study the order of magnitude of the Fourier transforms of certain Lipschitz functions on the Heisenberg group Hn. We compare our conclusions with some previous results in the field.
متن کاملFourier transform of a Gaussian measure on the Heisenberg group
An explicit formula is derived for the Fourier transform of a Gaussian measure on the Heisenberg group at the Schrödinger representation. Using this explicit formula, necessary and sufficient conditions are given for the convolution of two Gaussian measures to be a Gaussian measure.
متن کاملShannon Multiresolution Analysis on the Heisenberg Group *
We present a notion of frame multiresolution analysis on the Heisenberg group, abbreviated by FMRA, and study its properties. Using the irreducible representations of this group, we shall define a sinc-type function which is our starting point for obtaining the scaling function. Further, we shall give a concrete example of a wavelet FMRA on the Heisenberg group which is analogous to the Shannon...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1977
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.74.4.1328