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This volume contains translations of papers that originally appeared in the Japanese journal Sugaku. The papers range over a variety of topics, including operator algebras, analysis, and statistics.
Entrance to operator algebras by M. Takesaki Classification of $C*$-algebras by M. Izumi Weighted Hardy spaces and Jacobi series by A. Miyachi Legacy of J. Marcinkiewicz to real analysis in the 20th century by S. Igari The Kakeya conjecture by H. Tanaka Recent developments of analysis on fractals by T. Kumagai Symbolic dynamical system and number theoretical tilings by S. Akiyama Notions of independence in quantum probability and spectral analysis of graphs by N. Obata On various applications of the wavelet analysis to statistics by K. Tanaka Bhattacharyya type inequalities by H. Tanaka On an algebraic cone in C(^6) connected with rational curves by Ya. Y. Gadis and S. G. Gindikin.