Harmonic and Complex Analysis in Several Variables (eBook)

Steven G. Krantz (Autor)

eBook Download: PDF

2017 | 1st ed. 2017
XII, 424 Seiten
Springer International Publishing (Verlag)
978-3-319-63231-5 (ISBN)

Infos

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.

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.

Produkt-Details

• Erscheint lt. Verlag: 20.9.2017
• Reihe/Serie: Springer Monographs in Mathematics
• Reihe/Serie: Springer Monographs in Mathematics
• Zusatzinfo: XII, 424 p. 83 illus., 66 illus. in color.
• Verlagsort: Cham
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Schlagworte: admissible convergence • Bergman kernel • Bergman metric • Calderon-Zygmund theory • canonical kernels • Cauchy-Riemann equations • constructive kernels • d-bar Neumann Problem • finsler geometry • Folland-Stein theorem • Harmonic Analysis • Heisenberg group • holomorphic function • Monge-Ampere Equation • Paley-Wiener theorem • Poisson kernel • Prolegomena • reproducing kernels • Several Complex Variables • Szego integral
• ISBN-10: 3-319-63231-0 / 3319632310
• ISBN-13: 978-3-319-63231-5 / 9783319632315