Explorations in Harmonic Analysis

with Applications to Complex Function Theory and the Heisenberg Group

  • Steven G. Krantz

Part of the Applied and Numerical Harmonic Analysis book series (ANHA)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Steven G. Krantz
    Pages 1-13
  3. Steven G. Krantz
    Pages 15-33
  4. Steven G. Krantz
    Pages 35-47
  5. Steven G. Krantz
    Pages 49-60
  6. Steven G. Krantz
    Pages 61-81
  7. Steven G. Krantz
    Pages 83-109
  8. Steven G. Krantz
    Pages 111-131
  9. Steven G. Krantz
    Pages 133-178
  10. Steven G. Krantz
    Pages 179-229
  11. Steven G. Krantz
    Pages 231-248
  12. Steven G. Krantz
    Pages 249-264
  13. Back Matter
    Pages 265-360

About this book


This self-contained text provides an introduction to modern harmonic analysis in the context in which it is actually applied, in particular, through complex function theory and partial differential equations. It takes the novice mathematical reader from the rudiments of harmonic analysis (Fourier series) to the Fourier transform, pseudodifferential operators, and finally to Heisenberg analysis.

Within the textbook, the new ideas on the Heisenberg group are applied to the study of estimates for both the Szegö and Poisson–Szegö integrals on the unit ball in complex space. Thus the main theme of the book is also tied into complex analysis of several variables. With a rigorous but well-paced exposition, this text provides all the necessary background in singular and fractional integrals, as well as Hardy spaces and the function theory of several complex variables, needed to understand Heisenberg analysis.

Explorations in Harmonic Analysis is ideal for graduate students in mathematics, physics, and engineering. Prerequisites include a fundamental background in real and complex analysis and some exposure to functional analysis.


Fourier analysis Fourier transform Singular integral complex function theory harmonic analysis integral operators singular integrals

Authors and affiliations

  • Steven G. Krantz
    • 1
  1. 1.Dept. MathematicsWashington UniversitySt.LouisUSA

Bibliographic information