TY  - BOOK
AU  - Krantz,Steven G.
ED  - SpringerLink (Online service)
TI  - Explorations in Harmonic Analysis: with Applications to Complex Function Theory and the Heisenberg Group 
T2  - Applied and Numerical Harmonic Analysis
SN  - 9780817646691
U1  - 515.785 23
PY  - 2009///
CY  - Boston, MA
PB  - Birkhäuser Boston
KW  - MATHEMATICS
KW  - GROUP THEORY
KW  - HARMONIC ANALYSIS
KW  - FOURIER ANALYSIS
KW  - DIFFERENTIAL EQUATIONS, PARTIAL
KW  - ABSTRACT HARMONIC ANALYSIS
KW  - APPROXIMATIONS AND EXPANSIONS
KW  - SEVERAL COMPLEX VARIABLES AND ANALYTIC SPACES
KW  - GROUP THEORY AND GENERALIZATIONS
KW  - PARTIAL DIFFERENTIAL EQUATIONS
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/978-0-8176-4669-1
ER  -