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Clifford Algebras and their Applications in Mathematical Physics pp 215–219Cite as

A note on generalized Rademacher and hyperbolic functions

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Part of the book series: Fundamental Theories of Physics ((FTPH,volume 47))

Abstract

Recently a relation of Walsh functions system to Clifford algebras was noticed and applied in [2]. Due to this relation not only Clifford algebras but also Walsh functions might be applied to study spin lattice systems.

The intrinsic relation between generalized Walsh functions and generalized Clifford algebras as well as importance of hyperbolic functions altogether with generalized Clifford algebras for spin lattice systems is revealed in [3,4].

Here we discuss a specific relation between generalized Rademacher and hyperbolic functions. Rademacher functions form the set of generators for the group of Walsh functions.

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References

  1. Kac, M. (1959)’ statistical Independence in Probability Analysis and Number Theory’.

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  2. The Cams Mathematical Monographs, The Mathematical Association of America.

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  3. Hagmark, P.E., Lounesto P., NATO ASI (1986) ‘Series C: Math. and Phys. Sciences 183, 631–540.

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  4. Kwasniewski, A.K. (1988) ‘On Maximally Graded Algebras and Walsh Functions’, Reports on Math. Phys. Vol. 26, 137.

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  5. Kwasniewski, A.K. (1986) J. Phys. A: Math. Gen. 19, 1469-1476.

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  6. Kwasniewski, A.K. (1988) ‘Algebraic Properties of the 3-state Vector Potts Model’, Reports on Math. Phys. Vol. 26, 191.

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Author information

Authors and Affiliations

  1. Warsaw University, 15-424 Bialystok, Lipova 41, Poland

    A. K. Kwasniewski

Authors
  1. A. K. Kwasniewski
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Editor information

Editors and Affiliations

  1. Department of Mathematical Sciences, Applied Algebra, Université Montpellier II, Montpellier, France

    A. Micali

  2. Unité de Formation et de Recherche de Mathématiques Informatique Mécanique, Université de Provence, Marseille, France

    R. Boudet

  3. Laboratoire de Mathématiques Pures, Fourier Institute, Université de Grenoble I, Saint-Martin-d’Hères, France

    J. Helmstetter

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© 1992 Springer Science+Business Media Dordrecht

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Kwasniewski, A.K. (1992). A note on generalized Rademacher and hyperbolic functions. In: Micali, A., Boudet, R., Helmstetter, J. (eds) Clifford Algebras and their Applications in Mathematical Physics. Fundamental Theories of Physics, vol 47. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-8090-8_23

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  • DOI: https://doi.org/10.1007/978-94-015-8090-8_23

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4130-2

  • Online ISBN: 978-94-015-8090-8

  • eBook Packages: Springer Book Archive

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