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This book treats spherical harmonic expansion of real analytic functions and hyper functions on the sphere. Because a one-dimensional sphere is a circle, the simplest example of the theory is that of Fourier series of periodic functions. The author first introduces a system of complex neighborhoods of the sphere by means of the Lie norm. He then studies holomorphic functions and analytic functionals on the complex sphere. In the one-dimensional case, this corresponds to the study of holomorphic functions and analytic functionals on the annular set in the complex plane, relying on the Laurent series expansion. In this volume, it is shown that the same idea still works in a higher-dimensional sphere. The Fourier-Borel transformation of analytic functionals on the sphere is also examined; the eigenfunction of the Laplacian can be studied in this way.
Del 79 - Advanced Studies in Pure Mathematics
Mathematics Of Takebe Katahiro And History Of Mathematics In East Asia - Proceedings Of The International Conference On Traditional Mathematics In East Asia And Related Topics
Inbunden, Engelska, 2019
1 185 kr
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This volume is a collection of papers contributed by participants at the "International Conference on Traditional Mathematics in East Asia and Related Topics" held August 25-30, 2014 at Ochanomizu University, Tokyo, Japan, which was one of the satellite conferences of the Seoul ICM 2014. The year 2014 also coincides with the 350th anniversary of the birth of Takebe Katahiro (1664-1739), one of the great mathematicians of the Edo period. In his honor, the conference was called the "Takebe Conference 2014."This volume is divided into four parts and an appendix. Part one is concerned with Takebe Katahiro, his mathematics and his times. The editors believe that wasan represents one phase of the mathematics of East Asia, especially of China, Japan and Korea, for which ancient Chinese mathematics served as a basis, and Chinese characters as a lingua franca. Part two concerns the old mathematics of Korea in the Joseon Dynasty. Part three treats the mathematics of Ancient China. Part four, finally, follows the subsequent development of Japanese mathematics and mathematical education after the Meiji Restoration (1868). The very substantial appendix contains English translations of three volumes (12, 17 and 19) of the Taisei Sankei (twenty volumes, 1711), a monograph written by the master mathematician Seki Takakazu and the two Takebe brothers, Kata'akira and Katahiro.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America