関数解析的手法による位相力学系の研究

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(1) S. Kawamura who is the head investigator organized two workshops in UNCC and Yamagata University in the beginning and the end of 1999 respectively. Moreover he studied chaotic maps on metric measure space. As a way of studying he used the theory of operator algebras and obtained some important results concerning chaos maps and wavelets theory.(2) J. Tomiyama has clarified the structure of bounded orbit equivalence of topological dynamical systems for the interplay between topolocicl dynamics and C*-theory. He also classified the ideals of homeomorphism C*-algebras to show their structure in connection with the general isomorphism problem.(3) F. Uchida showed behavior of smooth actions of non-compact semi-simple Lie groups. Moreover he clarified construction and classification concerning smooth actions of Sp(p,q) on the (4p+4q-1)-sphere.(4) T. Okayasu obtained some important results concerning Lowener-Hainz inequalties in Banach*-algebras and a multivariable von Neumann's inequality.(5) S. Mori proved, for any given transcendental meromorphic mapping of CィイD1mィエD1 into PィイD1nィエD1(C), that one can eliminate all defects (deficient hyperplanes, deficient hypersurfaces) and defects of rational moving targets by a small deformation of the mapping, and also proved that meromorphic mappings without defects in dense in a space of transcendental meromorphic mappings.(6) E. Sato studied the Banach algebra M(p,q), which is defined by the translation invariant operators from Lp(G) to Lq(G) on infinite compact abelian groups. Also I studied the transference of continuity from maximal Fourier multiplier operators on n-dimensional Euclidian space to those on n-dimensional torus.