This book is a continuation of Volume I of the same title [Grund lehren der mathematischen Wissenschaften, Band 115 ]. We constantly 1 1. The textbook Real and cite definitions and results from Volume abstract analysis by E. HEWITT and K. R. STROMBERG [Berlin * Gottin gen *Heidelberg: Springer-Verlag 1965], which appeared between the publication of the two volumes of this work, contains many standard facts from analysis. We use this book as a convenient reference for such facts, and denote it in the text by RAAA. Most readers will have only occasional need actually to read in RAAA. Our goal in this volume is to present the most important parts of harmonic analysis on compact groups and on locally compact Abelian groups. We deal with general locally compact groups only where they are the natural setting for what we are considering, or where one or another group provides a useful counterexample. Readers who are interested only in compact groups may read as follows: 27, Appendix D, 28-30 [omitting subheads (30.6)-(30.60)ifdesired], (31.22)-(31.25), 32, 34-38, 44. Readers who are interested only in locally compact Abelian groups may read as follows: 31-33, 39-42, selected Mis cellaneous Theorems and Examples in 34-38. For all readers, 43 is interesting but optional. Obviously we have not been able to cover all of harmonic analysis.

This is a book of Faith in the Father, Son, and Holy Spirit. It is meant to bring truth out in the open and inspire you to have a personal relationship with our Lord Jesus Christ. He has touched my life in so many ways that I couldn't list them all. Are you facing what seems like insurmountable obstacles, TRUST HIM. Are you seeking peace TRUST HIM. Are you searching for a purpose TRUST HIM. Are you looking for love TRUST HIM. Remember that God has a plan for you and it will be revealed to you when you are ready to accept His continuing efforts to TRUST HIM. JOY AND PEACE TO YOU

The estimated withdrawal use of water in the United States during 1955 was about 740,000 mgd (million gallons per day). Withdrawal use of water requires that it be removed from the ground or diverted from a stream or lake. In this report it is divided into five types: public supplies, rural, irrigation, self-supplied industrial, and waterpower. Consumptive use of water is the quantity discharged to the atmosphere or incorporated in the products of the process in which it was used. Only a small part of the water withdrawn for industry was consumed, but as much as 60 percent of the water withdrawn for irrigation may have been consumed. Of the water withdrawn in 1955 about 1,500,000 mgd was for generation of waterpower, and all other withdrawal uses amounted to only about 240,000 mgd. Surface-water sources supplied 194,000 mgd and groundwater sources supplied 46,000 mgd. The amount of water withdrawn in each State and in each of 19 geographic regions is given. The quantity of water used without being withdrawn for such purposes as navigation, recreation, and conservation of fish and wildlife was not determined. The water surface area of the reservoirs and lakes used to store water for these purposes is sufficiently large that the evaporation from this source is greater than the quantity of water withdrawn for rural and public supplies. The amount of water used for generation of waterpower has increased 36 percent since 1950. The largest increase, 43 percent, was in self-supplied industrial water. Rural use, excluding irrigation, decreased 31 percent. The upper limit of our water supply is the average annual runoff, nearly 1,200, 000 mgd. The supply is depleted by the quantity of water consumed rather than by the quantity withdrawn. In 1955 about one-fourth of the water withdrawn was consumed. The amount thus consumed is about one-twentieth of the supply.