Harmonic and Complex Analysis in Several Variables

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 is one of Springer's and Birkhäuser's most prolific and popular authors in the field of functional analysis, geometric analysis, and partial differential equations. Krantz is the series editor of Birkhäuser's ' Cornerstones' graduate text series and the founder and editor-in-chief of "The Journal of Geometric Analysis", considered a society journal previously published by the AMS and often acts as an advisor to several senior editors at Springer/ Birkhäuser . He is also editor-in-chief of the "Journal of Mathematical Analysis and Applications". Professor Krantz is currently the editor-in-chief of the AMS Notices and also edits for "The American Mathematical Monthly", "Complex Analysis and Elliptical Equations", and "The Bulletin of the American Mathematical Monthly". Krantz is also known for his wide breadth of expertise in several areas of mathematics such as harmonica analysis, differential geometry, and Lie groups, to name a few. Notable awards include Chauvenet Prize (1992), Beckenbach Book Award (1994), Kemper Prize (1994), Outstanding Academic Book Award (1998), Washington University Faculty Mentor Award (2007).

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.