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- W2963443068 abstract "We study the spectral expansion of the semigroup of a general stable process killed on the first exit from the positive half-line. Starting with the Wiener-Hopf factorization we obtain the q-resolvent density for the killed process, from which we derive the spectral expansion of the semigroup via the inverse Laplace transform. The eigenfunctions and co-eigenfunctions are given rather explicitly in terms of the double sine function and they give rise to a pair of integral transforms which generalize the classical Fourier sine transform. Our results provide the first explicit example of a spectral expansion of the semigroup of a non-symmetric Lévy process killed on the first exit from the positive half-line." @default.
- W2963443068 created "2019-07-30" @default.
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- W2963443068 date "2018-01-01" @default.
- W2963443068 modified "2023-09-30" @default.
- W2963443068 title "Spectral analysis of stable processes on the positive half-line" @default.
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- W2963443068 doi "https://doi.org/10.1214/18-ejp134" @default.
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