Conical Fourier-Borel transformations for harmonic functionals on the Lie ball

• Autorzy: Mitsuo Morimoto , Keiko Fujita
• Języki publikacji: EN

Abstrakty

EN

Let L(z) be the Lie norm on $\tilde{𝔼} = ℂ^{n+1}$ and L*(z) the dual Lie norm. We denote by $𝓞_Δ(\tilde{B}(R))$ the space of complex harmonic functions on the open Lie ball $\tilde{B}(R)$ and by $Exp_Δ(\tilde{𝔼}; (A,L*))$ the space of entire harmonic functions of exponential type (A,L*). A continuous linear functional on these spaces will be called a harmonic functional or an entire harmonic functional. We shall study the conical Fourier-Borel transformations on the spaces of harmonic functionals or entire harmonic functionals.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 1996
• Tom: 37
• Numer: 1
• Strony: 95-113

Daty

wydano

1996

Twórcy

autor

Mitsuo Morimoto

• Department of Mathematics, Sophia University, 7-1, Kioicho, Chiyoda-ku, Tokyo, 102 Japan

autor

Keiko Fujita

• Department of Mathematics, Sophia University, 7-1, Kioicho, Chiyoda-ku, Tokyo, 102 Japan

Bibliografia

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• [2] M. Morimoto, Analytic functionals on the sphere and their Fourier-Borel transformations, in: Complex Analysis, Banach Center Publications 11, PWN-Polish Scientific Publishers, Warsaw, 1983, 223-250.
• [3] M. Morimoto and K. Fujita, Analytic functionals and entire functionals on the complex light cone, to appear in Hiroshima Math. J., 25 (1995) or in 26 (1996).
• [4] C. Müller, Spherical Harmonics, Lecture Notes in Math., 17 (1966), Springer.
• [5] R. Wada, On the Fourier-Borel transformations of analytic functionals on the complex sphere, Tôhoku Math. J., 38 (1986), 417-432.
• [6] R. Wada, Holomorphic functions on the complex sphere, Tokyo J. Math., 11 (1988), 205-218.
• [7] R. Wada and M. Morimoto, A uniqueness set for the differential operator $Δ_z + λ^2$, Tokyo J. Math., 10 (1987), 93-105.