By Christopher D. Sogge
This complicated monograph is worried with sleek remedies of significant difficulties in harmonic research. the most topic of the ebook is the interaction among principles used to check the propagation of singularities for the wave equation and their opposite numbers in classical research. particularly, the writer makes use of microlocal research to review difficulties related to maximal capabilities and Riesz capability utilizing the so-called half-wave operator. to maintain the therapy self-contained, the writer starts off with a quick evaluation of Fourier research and likewise develops the mandatory instruments from microlocal research. This moment variation contains new chapters. the 1st provides Hörmander's propagation of singularities theorem and makes use of this to end up the Duistermaat-Guillemin theorem. the second one matters more moderen effects with regards to the Kakeya conjecture, together with the maximal Kakeya estimates acquired by means of Bourgain and Wolff.
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