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Two spaces of generalized functions based on harmonic polynomials

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1171)

Abstract

Two spaces of generalized functions on the unit sphere Ωq−1 ⊂ ℝq are introduced. Both types of generalized functions can be identified with suitable classes of harmonic functions. They are projective and inductive limits of Hilbert spaces. Several natural classes of continuous and continuously extendible operators are discussed: Multipliers, differentiations, harmonic contractions/expansions and harmonic shifts. The latter two classes of operators are "parametrized" by the full affine semigroup ℝn.

AMS Classifications

  • 46F05
  • 46F10
  • 31B05
  • 20G05

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References

  1. Eijndhoven, S.J.L. van, A theory of generalized functions based on one-parameter groups of unbounded self-adjoint operators. T.H.-Report 81-WSK-03, Eindhoven University of Technology.

    Google Scholar 

  2. Eijndhoven, S.J.L. van, J. de Graaf, P. Kruszynski, Dual systems of inductive-projective limits of Hilbertspaces originating from self-adjoint operators. Preprint. Department of Maths. Eindhoven University of Technology.

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  3. Graaf, J. de, A theory of generalized functions based on holomorphic semigroups. Part A: Introduction and Survey. Proceedings Koninklijke Nederlandse Academie van Wetenschappen, A86(4), 1983, 407–420.

    MATH  Google Scholar 

  4. Idem.,. Part B: Analyticity spaces, trajectory spaces and their pairing. Proc. KNAW. A87(2), 1984, 155–171.

    MATH  Google Scholar 

  5. Idem.,. Part C: Linear mappings, tensor products and Kernel theorems. Proc. KNAW. A87(2), 1984, 173–187.

    MATH  Google Scholar 

  6. Müller, C., Spherical Harmonics. Springer Lecture Notes in Mathematics, Vol. 17, Springer Verlag, Berlin etc. 1966.

    MATH  Google Scholar 

  7. Seidel, J.J., Spherical Harmonics and Combinatorics. Preprint, Memorandum 1981–07, Juni 1981, Eindhoven University of Technology.

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© 1985 Springer-Verlag

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de Graaf, J. (1985). Two spaces of generalized functions based on harmonic polynomials. In: Brezinski, C., Draux, A., Magnus, A.P., Maroni, P., Ronveaux, A. (eds) Polynômes Orthogonaux et Applications. Lecture Notes in Mathematics, vol 1171. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0076541

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  • DOI: https://doi.org/10.1007/BFb0076541

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16059-5

  • Online ISBN: 978-3-540-39743-4

  • eBook Packages: Springer Book Archive