Shigeo Akashi

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In 1957, Kolmogorov and Arnold gave a solution to the 13th problem which had been formulated by Hilbert in 1900. Actually, it is known that there exist many open problems which can be derived from the original problem. From the function-theoretic point of view, Hilbert’s 13th problem can be exactly characterized as the superposition representability problem(More)
A computational method giving upper hounds of e-entropy of stochastic processes satisfying Kolmogorov-Prokhorov’s condition is studied, in terms of Shannon’s entropy of the probability measures on C[O, 11 induced by these processes. Moreover, this method and Ohya’s fractal dimensions are applied to investigating the asymptotic behavior of e-entropy of such(More)
Almost all of the technical methods, which are used in the theory of nonlinear dynamical systems, originated in the theory of one dimensional dynamical systems. In this talk, a relation between nonlinear ergodic theorems, which are developed by Prof. Takahashi and other researchers, and the asymptotic behavior of one dimensional dynamical systems will be(More)
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