On bicomplex Fourier--Wigner transforms
We consider the $1$- and $2$-d bicomplex analogs of the classical Fourier--Wigner transform. Their basic properties, including Moyal's identity and characterization of their ranges giving rise to new bicomplex--polyanalytic functional spaces are discussed. Particular case of special window is a...
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| creator | Gourari, Aiad El Ghanmi, Allal Zine, Khalil |
| description | We consider the $1$- and $2$-d bicomplex analogs of the classical
Fourier--Wigner transform. Their basic properties, including Moyal's identity
and characterization of their ranges giving rise to new bicomplex--polyanalytic
functional spaces are discussed. Particular case of special window is also
considered. An orthogonal basis for the space of bicomplex--valued square
integrable functions on the bicomplex numbers is constructed by means of the
polyanalytic complex Hermite functions. |
| doi_str_mv | 10.48550/arxiv.1904.09440 |
| format | Article |
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Fourier--Wigner transform. Their basic properties, including Moyal's identity
and characterization of their ranges giving rise to new bicomplex--polyanalytic
functional spaces are discussed. Particular case of special window is also
considered. An orthogonal basis for the space of bicomplex--valued square
integrable functions on the bicomplex numbers is constructed by means of the
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Fourier--Wigner transform. Their basic properties, including Moyal's identity
and characterization of their ranges giving rise to new bicomplex--polyanalytic
functional spaces are discussed. Particular case of special window is also
considered. An orthogonal basis for the space of bicomplex--valued square
integrable functions on the bicomplex numbers is constructed by means of the
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Fourier--Wigner transform. Their basic properties, including Moyal's identity
and characterization of their ranges giving rise to new bicomplex--polyanalytic
functional spaces are discussed. Particular case of special window is also
considered. An orthogonal basis for the space of bicomplex--valued square
integrable functions on the bicomplex numbers is constructed by means of the
polyanalytic complex Hermite functions.</abstract><doi>10.48550/arxiv.1904.09440</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Complex Variables Mathematics - Functional Analysis |
| title | On bicomplex Fourier--Wigner transforms |
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