THE RIESZ TRANSFORM. PART I. TENSOR FUNCTIONS
WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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A coordinateless account of the elements of tensor algebra and tensor calculus and a brief account of the theory of generalized differential operators on differentiable manifolds is presented. In tensor calculus coordinates may be looked upon in two different ways first, as a description of manifolds in terms of lower dimensional ones second, as a nonmenclature of coordinate notations. The treatment is a synthetic one whereby the relations between manifold and surrounding space are emphasized rather than ignored. Proofs, when given, are simply outlined and become more explicit as the subject matter is developed.