Harmonic and Complex Analysis in Several Variables
Steven G. Krantz
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Naturwissenschaften, Medizin, Informatik, Technik / Analysis
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.
harmonic analysis, Bergman metric, constructive kernels, prolegomena, canonical kernels, Monge-Ampere equation, Folland-Stein theorem, Cauchy-Riemann equations, Bergman kernel, d-bar Neumann problem, several complex variables, Heisenberg group, Paley-Wiener theorem, reproducing kernels, admissible convergence, holomorphic function, Poisson kernel, Szego integral, Finsler geometry, Calderon-Zygmund theory