ID - 131907998 TI - Geometric harmonic analysis, I : a sharp divergence theorem with nontangential pointwise traces AU - Mitrea, Dorina AU - Mitrea, Irina AU - Mitrea, Marius PY - 2022 SN - 9783031059506 9783031059490 9783031059513 9783031059520 3031059506 PB - Cham, Switzerland : Springer, DB - UniCat KW - Functional analysis KW - Harmonic analysis. Fourier analysis KW - Mathematical analysis KW - analyse (wiskunde) KW - Fourierreeksen KW - functies (wiskunde) KW - mathematische modellen KW - wiskunde KW - Divergence theorem. KW - Functional analysis. KW - Anàlisi funcional UR - https://www.unicat.be/uniCat?func=search&query=sysid:131907998 AB - This monograph presents a comprehensive, self-contained, and novel approach to the Divergence Theorem through five progressive volumes. Its ultimate aim is to develop tools in Real and Harmonic Analysis, of geometric measure theoretic flavor, capable of treating a broad spectrum of boundary value problems formulated in rather general geometric and analytic settings. The text is intended for researchers, graduate students, and industry professionals interested in applications of harmonic analysis and geometric measure theory to complex analysis, scattering, and partial differential equations. Volume I establishes a sharp version of the Divergence Theorem (aka Fundamental Theorem of Calculus) which allows for an inclusive class of vector fields whose boundary trace is only assumed to exist in a nontangential pointwise sense. ER -