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Dual ultracontractivity and its applications

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Abstract

The ultracontractivity is well studied and several equivalent conditions are known. In this paper, we introduce the dual notion of the ultracontractivity, which we call the dual ultracontractivity. We give necessary and sufficient conditions for the dual ultracontractivity. As an application, we discuss one-dimensional diffusion processes. We can write the conditions for the dual ultracontractivity in terms of speed measures.

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Authors and Affiliations

  1. Department of Mathematics, Kyoto University, Kyoto, 606-8502, Japan

    Ichiro Shigekawa

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  1. Ichiro Shigekawa
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Correspondence to Ichiro Shigekawa.

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Shigekawa, I. Dual ultracontractivity and its applications. Front. Math. China 9, 899–928 (2014). https://doi.org/10.1007/s11464-014-0398-y

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  • DOI: https://doi.org/10.1007/s11464-014-0398-y

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