© 2017

Harmonic and Complex Analysis in Several Variables


Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Steven G. Krantz
    Pages 1-18
  3. Steven G. Krantz
    Pages 19-57
  4. Steven G. Krantz
    Pages 59-88
  5. Steven G. Krantz
    Pages 89-113
  6. Steven G. Krantz
    Pages 115-130
  7. Steven G. Krantz
    Pages 131-193
  8. Steven G. Krantz
    Pages 195-211
  9. Steven G. Krantz
    Pages 213-243
  10. Steven G. Krantz
    Pages 245-308
  11. Steven G. Krantz
    Pages 395-403
  12. Back Matter
    Pages 405-424

About this book


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.


Finsler geometry Monge-Ampere equation d-bar Neumann problem harmonic analysis several complex variables holomorphic function Poisson kernel admissible convergence Heisenberg group prolegomena Folland-Stein theorem Calderon-Zygmund theory Szego integral Paley-Wiener theorem reproducing kernels constructive kernels canonical kernels Bergman kernel Bergman metric Cauchy-Riemann equations

Authors and affiliations

  1. 1.Department of MathematicsWashington UniversitySaint LouisUSA

Bibliographic information

  • Book Title Harmonic and Complex Analysis in Several Variables
  • Authors Steven G. Krantz
  • Series Title Springer Monographs in Mathematics
  • Series Abbreviated Title Springer Monographs in Mathematics
  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-63229-2
  • Softcover ISBN 978-3-319-87503-3
  • eBook ISBN 978-3-319-63231-5
  • Series ISSN 1439-7382
  • Series E-ISSN 2196-9922
  • Edition Number 1
  • Number of Pages XII, 424
  • Number of Illustrations 17 b/w illustrations, 66 illustrations in colour
  • Topics Abstract Harmonic Analysis
    Functions of a Complex Variable
  • Buy this book on publisher's site


“A number of key ideas in the subject are displayed in this text. Obviously, this is a nice book that will be valuable for researchers and students.” (Luping Chen, Mathematical Reviews, August, 2019)