Hyperfunctions, formal groups and generalized Lipschitz summation formulas. (English) Zbl 1254.43008
The purpose of the paper is to establish a connection between hyperfunctions and some topics of mathematical physics and analytic number theory. The authors relate hyperfunctions with formal groups and generalizations of the classical Lipschitz formula. It involves new polylogarithmic rational functions constructed via the Fourier expansion of certain sequences of Bernoulli type polynomials related to the Lazard formal group. They finally study the class of Appell polynomials, that is a more general class of Bernoulli type polynomials, to construct associate families of hyperfunctions.
Reviewer: Dohan Kim (Seoul)
MSC:
| 43A35 | Positive definite functions on groups, semigroups, etc. |
| 46F15 | Hyperfunctions, analytic functionals |
| 43A55 | Summability methods on groups, semigroups, etc. |
| 33C65 | Appell, Horn and Lauricella functions |
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