Authored by a ranking authority in harmonic analysis of several complex variables, this book embodies a state-of-the-art entrée at the intersection of two important fields of research: complex analysis and harmonic analysis. Written with the graduate student in mind, it is assumed that the reader has familiarity with the basics of complex analysis of one and several complex variables as well as with real and functional analysis. The monograph is largely self-contained and develops the harmonic analysis of several complex variables from the first principles. The text includes copious examples, explanations, an exhaustive bibliography for further reading, and figures that illustrate the geometric nature of the subject. Each chapter ends with an exercise set. Additionally, each chapter begins with a prologue, introducing the reader to the subject matter that follows; capsules presented in each section give perspective and a spirited launch to the segment;preludes help put ideas into context. Mathematicians and researchers in several applied disciplines will find the breadth and depth of the treatment of the subject highly useful.

Written by an established authority in harmonic analysis of several complex variables Develops the harmonic analysis of several complex variables from the first principles Includes copious examples, explanations, and an exhaustive bibliography Contains several figures which illustrate the geometric nature of the subject Exercise sets at the end of each chapter are especially useful for graduate level students Includes supplementary material: sn.pub/extras

Autorentext
Steven G. Krantz was born in San Francisco, California in 1951. He received the B.A. degree from the University of California at Santa Cruz in 1971 and the Ph.D. from Princeton University in 1974. Krantz has taught at UCLA, Princeton University, Penn State, and Washington University in St. Louis. He was Chair of the latter department for five years. Krantz has had 9 Masters students and 20 Ph.D. students. He has written more than 135 books and more than 270 scholarly papers. He edits 5 journals, and is Managing Editor of 3. He is the founding editorof the Journal of Geometric Analysis. He is the creator, founder, and editor of the new journal Complex Analysis and its Synergies. Krantz has won the Chauvenet Prize, the Beckenbach Book Award, and the Kemper Prize. He was recently named to the Sequoia High School Hall of Fame. He is an AMS Fellow.

Inhalt
Preface.- 1. Introduction and Review.- 2. Boundary Behavior.- 3. The Heisenberg Group.- 4. Analysis on the Heisenberg Group.- 5. Reproducing Kernels.- 6. More on the Kernels.- 7. The Bergman Metric.- 8. Geometric and Analytic Ideas.- 9. Additional Analytic Topics.- 10. Cauchy-Riemann Equations Solution.- 11. A Few Miscellaneous Topics.- Bibliography.- Index.