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Reproducibility of linear and nonlinear input-output systems |
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| Authors: | Felix Albrecht Kevin A Grasse Nelson Wax |
| Affiliation: | Department of Mathematics, University of Illinois, Urbana-Champaign, Urbana, Illinois 61801 U.S.A.;Department of Mathematics, University of Oklahoma, Norman, Oklahoma 73069 U.S.A.;Department of Electrical Engineering, University of Illinois, Urbana-Champaign, Urbana, Illinois 61801 U.S.A. |
| Abstract: | An algebraic setting for the Roman-Rota umbral calculus is introduced. It is shown how many of the umbral calculus results follow simply by introducing a comultiplication map and requiring it to be an algebra map. The same approach is used to construct a q-umbral calculus. Our umbral calculus yields some of Andrews recent results on Eulerian families of polynomials as corollaries. The homogeneous Eulerian families are studied. Operator and functional expansions are also included. |
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