The Heisenberg group and the group Fourier transform of regular homogeneous distributions

• Autorzy: Susan Elizabeth Slome
• Języki publikacji: EN

Abstrakty

EN

We calculate the group Fourier transform of regular homogeneous distributions defined on the Heisenberg group, $H^n$. All such distributions can be written as an infinite sum of terms of the form $f(θ)\overline{w}^{-k}P(z)$, where $(z,t) ∈ ℂ^{n} × ℝ$, $w = |z|^2 - it$, $θ = arg(\overline{w/w)$ and P(z) is an element of an orthonormal basis for the spherical harmonics. The formulas derived give the Fourier transform of the distribution in terms of a smooth kernel of the variable θ and the Weyl correspondent of P.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2000
• Tom: 143
• Numer: 3
• Strony: 251-266

Daty

wydano

2000

otrzymano

1999-07-21

poprawiono

2000-08-22

Twórcy

autor

Susan Elizabeth Slome

• Goldman, Sachs & Co, One New York Plaza (45th floor), New York, NY 10004, U.S.A.

Bibliografia

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