Explorations in Harmonic Analysis with Applications to Complex Function Theory and the Heisenberg Group /

• Main Author: Krantz, Steven G. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston, 2009.
• Edition: 1.
• Series: Applied and Numerical Harmonic Analysis
• Subjects: Mathematics.; Group theory.; Harmonic analysis.; Approximation theory.; Fourier analysis.; Functions of complex variables.; Mathematical models.; Abstract Harmonic Analysis.; Fourier Analysis.; Mathematical Modeling and Industrial Mathematics.; Approximations and Expansions.; Several Complex Variables and Analytic Spaces.; Group Theory and Generalizations.

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 se...

Table of Contents:

• Ontology and History of Real Analysis
• The Central Idea: The Hilbert Transform
• Essentials of the Fourier Transform
• Fractional and Singular Integrals
• A Crash Course in Several Complex Variables
• Pseudoconvexity and Domains of Holomorphy
• Canonical Complex Integral Operators
• Hardy Spaces Old and New
• to the Heisenberg Group
• Analysis on the Heisenberg Group
• A Coda on Domains of Finite Type.