Shape Analysis, Lebesgue Integration and Absolute Continuity Connections
by Javier Bernal
Publisher: arXiv.org 2019
Number of pages: 82
As shape analysis of the form presented in Srivastava and Klassen's textbook 'Functional and Shape Data Analysis' is intricately related to Lebesgue integration and absolute continuity, it is advantageous to have a good grasp of the latter two notions. Accordingly, in these notes we review basic concepts and results about Lebesgue integration and absolute continuity.
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by D. Husemoller - Tata Institute of Fundamental Research
Contents: Exact Couples and the Connes Exact Couple; Abelianization and Hochschild Homology; Cyclic Homology and the Connes Exact Couple; Cyclic Homology and Lie Algebra Homology; Mixed Complexes, the Connes Operator B; and more.
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This book at the beginning graduate level will help students with primary interests elsewhere to acquire a facility with tools of a functional analytic flavor, say in harmonic analysis, numerical analysis, stochastic processes, or in physics.
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This manuscript provides a brief introduction to nonlinear functional analysis. As an application we consider partial differential equations and prove existence and uniqueness for solutions of the stationary Navier-Stokes equation.
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