Reproducing Kernels for Harmonic Besov Spaces on the Ball
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Abstract
Besov spaces of harmonic functions on the unit ball of R '' are defined by requiring Sufficiently high-order derivatives of functions lie in harmonic Bergman spaces. We compute the reproducing kernels of those Besov spaces that are Hilbert spaces. The kernels turn out to be weighted infinite sums of zonal harmonics and natural radial fractional derivatives of the Poisson kernel. To cite this article: S. Gergun et al., C. R. Acad. Sci. Paris, Ser. I 347 (2009). (C) 2009 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.
Description
Gergun, Secil/0000-0003-0952-3070; Ureyen, Adem Ersin/0000-0002-7009-3797; Kaptanoglu, H. Turgay/0000-0002-8795-4426
Keywords
Dirichlet, Radial Differential Operator, Spherical Harmonic, Drury-arveson, Radial differential operator, Besov, Hardy, Bergman space, Bergman Space, Reproducing Kernel Hilbert Space, Spherical harmonic, Reproducing Kernel Hilbert space, Integral representations, integral operators, integral equations methods in higher dimensions, harmonic functions on the unit ball, reproducing kernels, Besov spaces, Bergman spaces
Fields of Science
01 natural sciences, 0101 mathematics
Citation
Gergün, S., Kaptanoğlu, H.T., Üreyen, A.E. (2009). Reproducing kernels for harmonic Besov spaces on the ball. Comptes Rendus Mathematique, 347(13-14), 735-738. http://dx.doi.org/10.1016/j.crma.2009.04.016
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OpenCitations Citation Count
13
Volume
347
Issue
13-14
Start Page
735
End Page
738
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Scopus : 12
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