Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces.

Chun Li; Alan McIntosh; Tao Qian

Displaying similar documents to “Clifford algebras, Fourier transforms and singular convolution operators on Lipschitz surfaces.”

Exotic parametrization problems

Leon Ehrenpreis (1993)

Annales de l'institut Fourier

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Non-holomorphic functional calculus for commuting operators with real spectrum

Mats Andersson, Bo Berndtsson (2002)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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We consider $n$ -tuples of commuting operators $a = a_{1}, ..., a_{n}$ on a Banach space with real spectra. The holomorphic functional calculus for $a$ is extended to algebras of ultra-differentiable functions on $ℝ^{n}$ , depending on the growth of $∥ exp (i a \cdot t) ∥$ , $t \in ℝ^{n}$ , when $| t | \to \infty$ . In the non-quasi-analytic case we use the usual Fourier transform, whereas for the quasi-analytic case we introduce a variant of the FBI transform, adapted to ultradifferentiable classes.

Morera type problems in Clifford analysis.

Emilio Marmolejo Olea (2001)

Revista Matemática Iberoamericana

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The Pompeiu and the Morera problems have been studied in many contexts and generality. For example in different spaces, with different groups, locally, without an invariant measure, etc. The variations obtained exhibit the fascination of these problems. In this paper we present a new aspect: we study the case in which the functions have values over a Clifford Algebra. We show that in this context it is completely natural to consider the Morera problem and its variations....