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In the end of the last century, Oliver Heaviside inaugurated an operational calculus in connection with his researches in electromagnetic theory. In his operational calculus, the operator of differentiation was denoted by the symbol "p." The explanation of this operator p as given by him was difficult to understand and to use, and the range of the valid- ity of his calculus remains unclear still now, although it was widely noticed that his calculus gives correct results in general. In the 1930s, Gustav Doetsch and many other mathematicians began to strive for the mathematical foundation of...

Kosaku Yosida, born on February 7, 1909, was brought up in Tokyo. Having majored in Mathematics at University of Tokyo, he was appointed to Assistant at Osaka University in 1933 and promoted to Associate Professor in 1934. He re ceived the title of Doctor of Science from Osaka University in 1939. In 1942 he was appointed to Professor at Nagoya University, where he worked very hard with his colleagues to promote and expand the newly established Department of Mathe matics. He was appointed to Professor at Osaka University in 1953 and then to Professor at University of Tokyo in 1955. After...

The present book is based on lectures given by the author at the University of Tokyo during the past ten years. It is intended as a textbook to be studied by students on their own or to be used in a course on Functional Analysis, i. e., the general theory of linear operators in function spaces together with salient features of its application to diverse fields of modern and classical analysis. Necessary prerequisites for the reading of this book are summarized, with or without proof, in Chapter 0 under titles: Set Theory, Topo logical Spaces, Measure Spaces and Linear Spaces. Then, starting...