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

Banach Center Publications (1996)

- Volume: 37, Issue: 1, page 95-113
- ISSN: 0137-6934

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topMorimoto, Mitsuo, and Fujita, Keiko. "Conical Fourier-Borel transformations for harmonic functionals on the Lie ball." Banach Center Publications 37.1 (1996): 95-113. <http://eudml.org/doc/208621>.

@article{Morimoto1996,

abstract = {Let L(z) be the Lie norm on $\tilde\{\} = ℂ^\{n+1\}$ and L*(z) the dual Lie norm. We denote by $_Δ(\tilde\{B\}(R))$ the space of complex harmonic functions on the open Lie ball $\tilde\{B\}(R)$ and by $Exp_Δ(\tilde\{\}; (A,L*))$ 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.},

author = {Morimoto, Mitsuo, Fujita, Keiko},

journal = {Banach Center Publications},

keywords = {dual Lie norm; space of complex harmonic functions on the open Lie ball; space of entire harmonic functions of exponential type; continuous linear functional; entire harmonic functional; conical Fourier-Borel transformations},

language = {eng},

number = {1},

pages = {95-113},

title = {Conical Fourier-Borel transformations for harmonic functionals on the Lie ball},

url = {http://eudml.org/doc/208621},

volume = {37},

year = {1996},

}

TY - JOUR

AU - Morimoto, Mitsuo

AU - Fujita, Keiko

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

JO - Banach Center Publications

PY - 1996

VL - 37

IS - 1

SP - 95

EP - 113

AB - Let L(z) be the Lie norm on $\tilde{} = ℂ^{n+1}$ and L*(z) the dual Lie norm. We denote by $_Δ(\tilde{B}(R))$ the space of complex harmonic functions on the open Lie ball $\tilde{B}(R)$ and by $Exp_Δ(\tilde{}; (A,L*))$ 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.

LA - eng

KW - dual Lie norm; space of complex harmonic functions on the open Lie ball; space of entire harmonic functions of exponential type; continuous linear functional; entire harmonic functional; conical Fourier-Borel transformations

UR - http://eudml.org/doc/208621

ER -

## References

top- [1] K. Ii, On a Bargmann-type transform and a Hilbert space of holomorphic functions, Tôhoku Math. J., 38 (1986), 57-69. Zbl0663.58016
- [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). Zbl0869.46020
- [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. Zbl0649.46038
- [6] R. Wada, Holomorphic functions on the complex sphere, Tokyo J. Math., 11 (1988), 205-218. Zbl0656.32002
- [7] R. Wada and M. Morimoto, A uniqueness set for the differential operator ${\Delta}_{z}+{\lambda}^{2}$, Tokyo J. Math., 10 (1987), 93-105. Zbl0641.32005

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