The book discusses the extensions of basic Fourier Analysis techniques to the Clifford
algebra framework. Topics covered: construction of Clifford-valued wavelets, Calderon …

It is assumed that the reader has a basic knowledge of metric spaces, topology, measure
theory, and the theory of bounded linear operators on Banach and Hilbert spaces. Suitable …

In the Fourier theory of functions of one variable, it is common to extend a function and its
Fourier transform holomorphically to domains in the complex plane C, and to use the power …

This is a slightly expanded version of my lectures at the conference on Clifford Algebras in
Analysis held in Fayetteville, Arkansas. I present an exposition of basic material on Clifford …

We prove quadratic estimates for complex perturbations of Dirac-type operators, and thereby
show that such operators have a bounded functional calculus. As an application we show …

We consider boundary value problems for the heat equation in time-varying graph domains
of the form Ω={(x_0,x,t)∈R*R^n-1*R:x_0>A(x,t)\}, obtaining solvability of the Dirichlet and …

Dirac operators play an important role in several domains of mathematics and physics, for
example: index theory, elliptic pseudodifferential operators, electromagnetism, particle …

In this paper we extend the H∞ functional calculus to quaternionic operators and to n-tuples
of noncommuting operators using the theory of slice hyperholomorphic functions and the …

We present a simple, Clifford algebra‐based approach to several key results in the theory of
Maxwell's equations in non‐smooth subdomains of ℝm. Among other things, we give new …

The classical formulation of boundary value problems for constant coefficient elliptic
operators, or systems of operators, involves continuous data on the boundary of a (smooth) …