This new book contains the most up-to-date and focused description
of the applications of Clifford algebras in analysis, particularly
classical harmonic analysis. It is the first single volume devoted
to applications of Clifford analysis to other aspects of
analysis.
All chapters are written by world authorities in the area. Of
particular interest is the contribution of Professor Alan McIntosh.
He gives a detailed account of the links between Clifford algebras,
monogenic and harmonic functions and the correspondence between
monogenic functions and holomorphic functions of several complex
variables under Fourier transforms. He describes the correspondence
between algebras of singular integrals on Lipschitz surfaces and
functional calculi of Dirac operators on these surfaces. He also
discusses links with boundary value problems over Lipschitz
domains.
Other specific topics include Hardy spaces and compensated
compactness in Euclidean space; applications to acoustic scattering
and Galerkin estimates; scattering theory for orthogonal wavelets;
applications of the conformal group and Vahalen matrices; Newmann
type problems for the Dirac operator; plus much, much more
Clifford Algebras in Analysis and Related Topics also contains the
most comprehensive section on open problems available. The book
presents the most detailed link between Clifford analysis and
classical harmonic analysis. It is a refreshing break from the many
expensive and lengthy volumes currently found on the subject.
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