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Abstrakty
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.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Numer
Strony
251-266
Opis fizyczny
Daty
wydano
2000
otrzymano
1999-07-21
poprawiono
2000-08-22
Twórcy
autor
- Goldman, Sachs & Co, One New York Plaza (45th floor), New York, NY 10004, U.S.A.
Bibliografia
- [1] H. Bateman, Higher Transcendental Functions, McGraw-Hill, 1953.
- [2] D. Geller, Some results in $H^p$ theory for the Heisenberg group, Duke Math. J. 47 (1980), 365-390.
- [3] D. Geller, Fourier analysis on the Heisenberg group I: Schwartz space, J. Funct. Anal. 36 (1980), 205-254.
- [4] D. Geller, Local solvability and homogeneous distributions on the Heisenberg group, Comm. Partial Differential Equations 5 (1980), 475-560.
- [5] D. Geller, Spherical harmonics, the Weyl transform and the Fourier transform on the Heisenberg group, Canad. J. Math. 36 (1984), 615-684.
- [6] D. Geller, Analytic Pseudodifferential Operators for the Heisenberg Group and Local Solvability, Math. Notes 37, Princeton Univ. Press, 1990.
- [7] M. Reed and B. Simon, Methods of Modern Mathematical Physics. I. Functional Analysis, Academic Press, 1980.
- [8] E. Stein, Harmonic Analysis, Princeton Math. Ser. 43, Monogr. Harmonic Anal. III, Princeton Univ. Press, 1993.
- [9] E. Stein and G. Weiss, Introduction to Fourier Analysis on Euclidean Spaces, Princeton Math. Ser. 32, Princeton Univ. Press, 1971.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv143i3p251bwm