Hille E. Methods in classical and functional analysis

Addison Wesley Publishing, 1972. — 294 p.
The book was originally planned as an elementary introduction to functional analysis, but in working out the guiding ideas I soon found that my program took in only part of what nowadays goes under the title of functional analysis. On the other hand, applications to analysis were stressed and unvarnished classical analysis was handed out in significant doses. My interests have always been toward the concrete sides of analysis, a tendency that has not become less pronounced with the years.
Practically (he whole hook has been lecture material given from Bombay to Kingston, R.I., under varying titles. The book is not polished; there are loose ends and many unsolved problems waiting for the craftsman. Such research openings occur chiefly in the last four chapters. There are over 850 exercises, a fair part of which are byproducts of the author's own research. While problem solving should not become an obsession, it provides good training in research and stimulates an inquisitive mind to venture into new directions.
The material in the book can serve several different purposes. Chapters 1 to 4 and 7 to 11 can serve as text for an introductory course in functional analysis. In the author's judgment it offers a fairly easy introduction and supplement to the more advanced books such as Dunford-Schwartz, Hille—Phillips, and Yosida. Chapters 5, 6, and 12 through 15 stand closer to classical analysis than does the rest of the book and can serve as a text for a course in aspects of analysis.