forked from pzorin/decoupling-lecture-notes
-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathdecoupling-notes.tex
More file actions
121 lines (101 loc) · 3.05 KB
/
Copy pathdecoupling-notes.tex
File metadata and controls
121 lines (101 loc) · 3.05 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
\documentclass[11pt,oneside]{article}
\usepackage{ifxetex,ifluatex}
\newif\ifxetexorluatex
\ifxetex
\xetexorluatextrue
\else
\ifluatex
\xetexorluatextrue
\else
\xetexorluatexfalse
\fi
\fi
\ifxetexorluatex
\usepackage{fontspec}
\ifxetex
\usepackage{xltxtra}
\fi
\defaultfontfeatures{Mapping=tex-text}
\usepackage{unicode-math}
\setmainfont{STIX Two Text}[Ligatures={Common}]
\setmathfont{STIX Two Math}
\PassOptionsToPackage{unicode,psdextra}{hyperref}
\else
\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
\fi
\usepackage{microtype}
\usepackage{hyperref}
\hypersetup{
pdfstartview=FitH,
pdfauthor={Pavel Zorin-Kranich},
pdftitle={Lecture notes on decoupling},
pdfborder={0 0 0},
bookmarks=true,
unicode
}
\def\C{\mathbb{C}} % redefined by hyperref
\usepackage[paperheight=279mm,paperwidth=16cm,textheight=26cm,textwidth=14cm]{geometry}
\usepackage[english]{babel}
\usepackage[style=alphabetic]{biblatex}
\addbibresource{decoupling.bib}
\usepackage{amsxtra}
\usepackage{graphicx}
\usepackage{booktabs}
\usepackage{tikz}
\input{macros.tex}
\newcommand{\MlRs}{\mathrm{MlRs}}
% Maximal Schr\"odinger
\newcommand{\eit}{e^{i t \Delta}}
\newcommand{\eir}{e^{i r \Delta}}
\newcommand{\RefStr}{\mathrm{RefStr}}
\newcommand{\MultRefStr}{\mathrm{MultRefStr}}
\newcommand{\FrStr}{\mathrm{FrStr}}
\newcommand{\bB}{\mathfrak{B}} % ball Big
\newcommand{\bM}{\mathfrak{M}} % ball Medium
\newcommand{\bS}{\mathfrak{S}} % ball Smal
\newcommand{\bBp}{\mathfrak{B}'} % ball Big previous scale
\newcommand{\bMp}{\mathfrak{M}'} % ball Medium previous scale
\newcommand{\bSp}{\mathfrak{S}'} % ball Small previous scale
\newcommand{\bO}{\mathfrak{O}} % ball Out
\newcommand{\bI}{\mathfrak{I}} % ball In
\newcommand{\bOp}{\mathfrak{O}'} % ball Out previous scale
\newcommand{\bIp}{\mathfrak{I}'} % ball In previous scale
%% brascamp-lieb notation
\renewcommand{\div}{\operatorname{div}}
\newcommand{\diag}{\operatorname{diag}}
\def\p{\bfp}
\def\A{\bfA}
\def\f{\bff}
% Moment curve
\newcommand{\level}{\mathcal{V}}
\newcommand{\sublevel}{\mathcal{S}}
\newcommand{\upset}{{\uparrow}} % This is a unary operator. The inner pair of braces in needed for correct spacing.
\newcommand{\Dset}{\mathcal{D}}
\begin{document}
\setcounter{section}{-1}
\title{Lecture notes on Fourier Decoupling}
\author{Pavel Zorin-Kranich}
\maketitle
\begin{center}
University of Bonn, summer term 2019
\end{center}
This work is licensed under the Creative Commons Attribution 4.0 International License.
To view a copy of this license, visit \url{http://creativecommons.org/licenses/by/4.0/} or send a letter to Creative Commons, PO Box 1866, Mountain View, CA 94042, USA.
\tableofcontents
\input{00-intro.tex}
\input{01-mult-kakeya.tex}
\input{02-mult-restriction.tex}
\input{03-dec-paraboloid.tex}
\input{04-local-smoothing.tex}
\input{05-cone-square-fct.tex}
\input{06-reverse-square-fct.tex}
\input{07-max-schroedinger.tex}
\input{08-brascamp-lieb.tex}
\input{09-dec-moment-curve.tex}
\appendix
\input{10-weyl-sums.tex}
\input{92-kakeya-2d.tex}
\input{93-cordoba-square-fct.tex}
\printbibliography[heading=bibintoc]
\end{document}