• Corpus ID: 248495946

Fractional Poisson Analysis in Dimension one

  title={Fractional Poisson Analysis in Dimension one},
  author={Jerome B. Bendong and Sheila Menchavez and Jos{\'e} Lu{\'i}s da Silva},
In this paper, we use a biorthogonal approach (Appell system) to construct and characterize the spaces of test and generalized functions associated to the fractional Poisson measure π λ,β , that is, a probability measure in the set of natural (or real) numbers. The Hilbert space L 2 ( π λ,β ) of complex-valued functions plays a central role in the construction, namely, the test function spaces ( N ) κπ λ,β , κ ∈ [0 , 1] is densely embedded in L 2 ( π λ,β ) . Moreover, L 2 ( π λ,β ) is also… 

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