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Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)$
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Isroil A. Ikromov and Detlef Müller

Print publication date: 2016

Print ISBN-13: 9780691170541

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691170541.001.0001

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Proofs of Propositions 1.7 and 1.17

Proofs of Propositions 1.7 and 1.17

Chapter:
(p.244) Chapter Nine Proofs of Propositions 1.7 and 1.17
Source:
Fourier Restriction for Hypersurfaces in Three Dimensions and Newton Polyhedra (AM-194)
Author(s):

Isroil A. Ikromov

Detlef Müller

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691170541.003.0009

This chapter showcases the remaining proofs of two results from the first chapter. It turns to the first of these results, based on a proposition made Chapter 1, on the characterization of linearly adapted coordinates. The chapter separately proves the two conditions discussed in the first proposition, before moving on to the next proposition. The second proposition obtained from Chapter 1 is about an invariant description of the notion of r-height. The chapter proves both parts of the proposition at the same time, which proves in the process an inequality from Chapter 9 before arriving at the proof of the proposition proper.

Keywords:   linearly adapted coordinates, invariant description, r-height, propositions, Newton polyhedron

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