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

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.

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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 Szeg? and Poisson–Szeg? 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.

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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 Szeg? and Poisson–Szeg? 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.

Content:
Front Matter....Pages I-XIV
Ontology and History of Real Analysis....Pages 1-13
The Central Idea: The Hilbert Transform....Pages 15-33
Essentials of the Fourier Transform....Pages 35-47
Fractional and Singular Integrals....Pages 49-60
A Crash Course in Several Complex Variables....Pages 61-81
Pseudoconvexity and Domains of Holomorphy....Pages 83-109
Canonical Complex Integral Operators....Pages 111-131
Hardy Spaces Old and New....Pages 133-178
Introduction to the Heisenberg Group....Pages 179-229
Analysis on the Heisenberg Group....Pages 231-248
A Coda on Domains of Finite Type....Pages 249-264
Back Matter....Pages 265-360

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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 Szeg? and Poisson–Szeg? 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.

Content:
Front Matter....Pages I-XIV
Ontology and History of Real Analysis....Pages 1-13
The Central Idea: The Hilbert Transform....Pages 15-33
Essentials of the Fourier Transform....Pages 35-47
Fractional and Singular Integrals....Pages 49-60
A Crash Course in Several Complex Variables....Pages 61-81
Pseudoconvexity and Domains of Holomorphy....Pages 83-109
Canonical Complex Integral Operators....Pages 111-131
Hardy Spaces Old and New....Pages 133-178
Introduction to the Heisenberg Group....Pages 179-229
Analysis on the Heisenberg Group....Pages 231-248
A Coda on Domains of Finite Type....Pages 249-264
Back Matter....Pages 265-360
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