Excursions in Harmonic Analysis, Volume 6: In Honor of John Benedetto’s 80th Birthday (Applied and Numerical Harmonic Analysis)

ANHA Series Preface
Foreword
Preface
Contents
Contributors
Acronyms
Part I Introduction
	John Benedetto's Mathematical Work
		1 Brief Biography
		2 Coda
		3 PhD Theses
		4 Papers
		List of John J. Benedetto's Published Papers
Part II Harmonic Analysis
	Absolute Continuity and the Banach–Zaretsky Theorem
		1 Introduction
			1.1 The Fundamental Theorem of Calculus
			1.2 Notation
		2 Differentiation
			2.1 Functions of Bounded Variation
			2.2 Our Failure: Differentiability of Monotone Increasing Functions
			2.3 The Simple Vitali Lemma
			2.4 The Lebesgue Differentiation Theorem
		3 The Fundamental Theorem of Calculus
			3.1 The Simple Version of the FTC
			3.2 Absolute Continuity
			3.3 The Growth Lemmas
			3.4 The Banach–Zaretsky Theorem
			3.5 Corollaries
			3.6 The Fundamental Theorem of Calculus
		References
	Spectral Synthesis and H1(R)
		1 Introduction
		2 Main Results
		References
	Universal Upper Bound on the Blowup Rate of Nonlinear Schrödinger Equation with Rotation
		1 Introduction
		2 Preliminaries
			2.1 Local Well-Posedness for p[1, 1+4/(n-2) )
			2.2 Radial Gagliardo–Nirenberg Inequality
		3 Localized Virial Identity
		4 Proof of the Main Theorem
		5 Numerical Results for Mass-Critical and Mass-Supercritical RNLS in 2D
		References
	Almost Eigenvalues and Eigenvectors of Almost Mathieu Operators
		1 Introduction
			1.1 Definitions and Notation
		2 Finite Hermite Functions as Approximate Eigenvectors of the Finite-Dimensional Almost Mathieu Operator
		3 Eigenanalysis of the Infinite Almost Mathieu Operator Hα,β,θ
		4 Numerical Simulations
		References
	Spatio–Spectral Limiting on Redundant Cubes: A Case Study
		1 Overview
		2  Cubes, Space Limiting and Spectrum Limiting
			2.1 Graph Laplacian and Graph Fourier Transform
			2.2 Cubes and Their Fourier Transforms
		3 Redundant Cubes
			3.1 Definition of Redundant Cubes and Laplacian Eigenvalues
			3.2 Neighborhood Limiting and Spectrum Limiting on Redundant Cubes
		4 SSL Results on BN and Outline of Current Approach
			4.1 Summary of Prior Results
			4.2 Summary of Present Approach
		5 Two Concrete Examples
			5.1 A Tiny Example: Z24 with Generators 1, 2, 4, 8, 3, 6, 12
			5.2 A Moderate Example
			5.3 Eigenvectors of Spatio–Spectral Limiting
		6 Adjacency on S
		References
Part III Wavelets and Frames
	A Notion of Optimal Packings of Subspaces with Mixed-Rank and Solutions
		1 Introduction
		2 Preliminaries
		3 Constant-Rank Packings Revisited
		4 Generalized to the Mixed-Rank Packing Problem
		5 Properties of Optimally Spread Mixed-Rank Packings
		6 Constructing Solutions
		References
	Construction of Frames Using Calderón–Zygmund Operator Theory
		1 Introduction
		2 Preliminaries and Some Lemmas
		3 Proof of Theorem 1.1
		References
	Equiangular Frames and Their Duals
		1 Introduction
		2 Construction and Existence of Equiangular Frames
		3 Nontight Equiangular Frames and Their Duals
			3.1 Examples of Nontight Equiangular Frames
			3.2 Frame Properties of Canonical Duals of Equiangular Frames
			3.3 Angle Sets of Canonical Duals of Equiangular Frames
		References
	Wavelet Sets for Crystallographic Groups
		1 Introduction
		2 Preliminaries
		3 Crystallographic Wavelet Sets
		4 Simple Crystallographic Wavelet Sets
		References
	Discrete Translates in Function Spaces
		1 Completeness of Translates
		2 Completeness of Discrete Translates in L2(R)
			2.1 Uniformly Discrete Spectra
			2.2 Schwartz Generators
		3 Completeness of Discrete Translates in Lp(R)
			3.1 The Case p>2
			3.2 The Case p=1
			3.3 The Case 1