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A central limit theorem for coalgebras

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1210)

Abstract

Using elementary properties of coalgebras, a limit theorem for linear functionals on a coalgebra is proved which generalizes several non-commutative central limit theorems [3, 5, 6, 9].

Keywords

  • Central Limit Theorem
  • Linear Functional
  • Pointwise Convergence
  • Algebra Homomorphism
  • Complex Vector Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Abe, E.: Hopf Algebras, Cambridge University Press (1980)

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  2. Bourbaki, N.: Elements of Mathematics, Algebra, Chap. III, Hermann, Paris (1973)

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  3. Canisius, J.: Algebraische Grenzwertsätze und unbegrenzt teilbare Funktionale, Diplomarbeit, Heidelberg (1979)

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  5. Giri, N. and von Waldenfels, W.: An Algebraic Version of the Central Limit Theorem, Z. Wahrscheinlichkeitstheorie verw. Gebiete 42, 129–134 (1978)

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  6. Hudson, R. L.: A Quantum-Mechanical Central Limit Theorem for Anti-Commuting Observables, J. Appl. Prob. 10, 502–509 (1973)

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  7. Schürmann, M.: Positive and Conditionally Positive Linear Functionals on Coalgebras, in Lect. Notes in Math. 1136, Springer, New York, Heidelberg, Berlin, 475–492 (1985)

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  8. Sweedler, M. E.: Hopf Algebras, Benjamin, New York (1969)

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  9. von Waldenfels, W.: An Algebraic Central Limit Theorem in the Anticommuting Case, Z. Wahrscheinlichkeitstheorie verw, Gebiete 42, 135–140 (1978)

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© 1986 Springer-Verlag

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Schürmann, M. (1986). A central limit theorem for coalgebras. In: Heyer, H. (eds) Probability Measures on Groups VIII. Lecture Notes in Mathematics, vol 1210. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0077181

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  • DOI: https://doi.org/10.1007/BFb0077181

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-16806-5

  • Online ISBN: 978-3-540-44852-5

  • eBook Packages: Springer Book Archive