Optical entangled fractional Fourier transform derived via non-unitary SU(2) bosonic operator realization and its convolution theorem

We introduce a new n-mode Bose operator realization of SU(2) Lie algebra and link it to the two mutually conjugate multipartite entangled state representations. In so doing we are naturally lead to the n-mode entangle fractional Fourier transform (EFFT), which provides us with a convenient way to deriving the EFFT of quantum-mechanical wave functions.

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TEOREMA KONVOLUSI PADA TRANSFORMASI FOURIER FRAKSIONAL QUATERNION SISI KIRI DAN SIFAT-SIFATNYA

JURNAL ILMIAH MATEMATIKA DAN TERAPAN ◽

10.22487/2540766x.2019.v16.i1.12732 ◽

2019 ◽

Vol 16 (1) ◽

pp. 1-12

Author(s):

N H Wibowo ◽

S Musdalifah ◽

Resnawati Resnawati

Keyword(s):

Fourier Transform ◽

Frequency Domain ◽

Quaternion Algebra ◽

Fractional Fourier Transform ◽

Convolution Theorem ◽

Quaternion Fourier Transform

Fourier transform (FT) is growing very rapidly and applying in various fields such as analyzing and decomposing signals in the frequency domain. FT has been extended to quaternion algebra known as the Quaternion Fourier Transform (QFT). The purpose of this paper are to formulate the definition and properties of the left sided Quaternion Fractional Fourier Transform (QFFT), to formulate the definition and convolution theorem for left sided QFFT. Firstly, the results showed the formulation of the left sided QFFT definition and some of the properties such as linearity, translation, modulation and scalar. Secondly, its showed the formulation of convolution theorem for left sided QFFT and also the left sided QFFT of conjugate and translation convolution.

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A Convolution Theorem for the Two Dimensional Fractional Fourier Transform in Generalized Sense

2010 3rd International Conference on Emerging Trends in Engineering and Technology ◽

10.1109/icetet.2010.46 ◽

2010 ◽

Author(s):

V D Sharma ◽

P B Deshmukh

Keyword(s):

Fourier Transform ◽

Fractional Fourier Transform ◽

Convolution Theorem ◽

Two Dimensional

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Quaternionic fractional Fourier transform for Boehmians

Ukrains’kyi Matematychnyi Zhurnal ◽

10.37863/umzh.v72i6.649 ◽

2020 ◽

Vol 72 (6) ◽

pp. 812-821

Author(s):

R. Roopkumar

Keyword(s):

Fourier Transform ◽

Fractional Fourier Transform ◽

Convolution Theorem

UDC 517.9 We construct a Boehmian space of quaternion valued functions using the quaternionic fractional convolution. Applying the convolution theorem, the quaternionic fractional Fourier transform is extended to the context of Boehmians and its properties are established.

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Fractional convolution

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s0334270000012509 ◽

1998 ◽

Vol 40 (2) ◽

pp. 257-265 ◽

Cited By ~ 19

Author(s):

David Mustard

Keyword(s):

Fourier Transform ◽

Fractional Fourier Transform ◽

Convolution Theorem ◽

Convolution Operators ◽

Double Integral ◽

Integral Formulas ◽

Wigner Distributions ◽

Fractional Unit

AbstractA continuous one-parameter set of binary operators on L2(R) called fractional convolution operators and which includes those of multiplication and convolution as particular cases is constructed by means of the Condon-Bargmann fractional Fourier transform. A fractional convolution theorem generalizes the standard Fourier convolution theorems and a fractional unit distribution generalizes the unit and delta distributions. Some explicit double-integral formulas for the fractional convolution between two functions are given and the induced operation between their corresponding Wigner distributions is found.

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Logarithmic uncertainty principle, convolution theorem related to continuous fractional wavelet transform and its properties on a generalized Sobolev space

International Journal of Wavelets Multiresolution and Information Processing ◽

10.1142/s0219691317500503 ◽

2017 ◽

Vol 15 (05) ◽

pp. 1750050 ◽

Cited By ~ 3

Author(s):

Mawardi Bahri ◽

Ryuichi Ashino

Keyword(s):

Fourier Transform ◽

Wavelet Transform ◽

Sobolev Space ◽

Inversion Formula ◽

Uncertainty Relation ◽

Fractional Fourier Transform ◽

Convolution Theorem ◽

Inner Product ◽

Fractional Wavelet Transform ◽

Product Relation

The continuous fractional wavelet transform (CFrWT) is a nontrivial generalization of the classical wavelet transform (WT) in the fractional Fourier transform (FrFT) domain. Firstly, the Riemann–Lebesgue lemma for the FrFT is derived, and secondly, the CFrWT in terms of the FrFT is introduced. Based on the CFrWT, a different proof of the inner product relation and the inversion formula of the CFrWT are provided. Thereafter, a logarithmic uncertainty relation for the CFrWT is investigated and the convolution theorem related to the CFrWT is established using the convolution of the FrFT. The CFrWT on a generalized Sobolev space is introduced and its important properties are presented.

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