an:02070069
Zbl 1045.32001
Fujita, Keiko; Morimoto, Mitsuo
Analytic functions and analytic functionals on some balls in the complex Euclidean space
EN
Begehr, Heinrich G. W. (ed.) et al., Analysis and applications--ISAAC 2001. \newline Proceedings of the 3rd international congress, Berlin, Germany, August 20--25, 2001. Dordrecht: Kluwer Academic Publishers (ISBN 1-4020-1384-1/hbk). Int. Soc. Anal. Appl. Comput. 10, 151-159 (2003).
2003
a
32A10 32A05
Lie norm; Euclidean norm; dual Lie norm; analytic functions; analytic functionals; homogeneous harmonic polynomials; inductive limit locally convex topology; growth behavior of harmonic components; double series expansion of holomorphic functions; entire functions of exponential type; Fourier-Borel transform
Generalizing the Lie norm, the Euclidean norm and the dual Lie norm, the authors define a series of norms \(\{N_p\}_{1\leq p\leq\infty}\) on \(\mathbb C^{n+1}\), consider holomorphic functions, entire functions of exponential type and analytic functionals on the \(N_p\)-balls \(\widetilde{B}_p(r)\), and characterize them by their growth behavior of their harmonic components in their double series expansion. By means of these results, the Martineau's theorem on Fourier-Borel transform is proved in the case of \(N_p\)-norm on the double series expansion.
For the entire collection see [Zbl 1031.35002].
Eleonora Storozhenko (Odessa)