Explorations in harmonic analysis: with applications to complex function theory and the Heisenberg group

This self-contained text provides an introduction to modern harmonic analysisin 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. Provides an introduction to a particular direction in modern harmonic analysis Self-contained texton analysis of integral operators Presents both fundamentals and applicationsof harmonic analysis, especially to important concepts about the Heisenberg group INDICE: Preface.- Background in Fourier Series.- The Fourier Transform.- Fractional and Singular Integrals.- Pseudodifferential Operators.- The Real Variable Point of View.- Several Complex Variables.- Canonical Integral Operators.- Boundary Behavior.- The Heisenberg Group.- Analysis on the Heisenberg Group.- Index.

• ISBN: 978-0-8176-4668-4
• Editorial: Birkhaüser
• Encuadernacion: Cartoné
• Páginas: 362
• Fecha Publicación: 01/06/2009
• Nº Volúmenes: 1
• Idioma: Inglés