Abstract

These theories constitute fascinating fields of application of the analytical theory of semi-groups. Mathematically speaking, the ergodic theory is concerned with the “time average” \(\mathop{{\lim }}\limits_{{t \uparrow \infty }} {t^{{ - 1}}}\int\limits_{0}^{t} {{T_{s}}ds}\) of a semi-group T t , and the diffusion theory is concerned with the investigation of a stochastic process in terms of the infinitesimal generator of the semi-group intrinsically associated with the stochastic process.

Keywords

Manifold Convolution Hunt 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1974

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Gakushuin UniversityTokyoJapan

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