Abstract
Without any assumptions on the space dimension or boundedness of the region, we prove -spectral independence of generators of -semigroups estimated by the positive -semigroup . In particular, if the semigroup is self-adjoint in , it is shown that only the estimate by is sufficient for -spectral independence. The proof depends on the idea of considering the spectra of the operators and applying the spectral independence result of B.A. Barnes for integral operators, where is the generator of the semigroup in question.
Acknowledgments
The authors would like to thank the referee for useful comments.
Citation
Shizuo Miyajima. Hisakazu Shindoh. "Gaussian estimates of order and -spectral independence of generators of -semigroups II." SUT J. Math. 42 (2) 357 - 371, June 2006. https://doi.org/10.55937/sut/1173206041
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