Intro
ANHA Series Preface
Preface
Contents
Contributors
Part I Introduction to This Volume
1 From Strichartz Estimates to Differential Equations on Fractals
1.1 Functional and Harmonic Analysis on Euclidean Spaces
1.1.1 Harmonic Analysis and Sobolev Spaces
1.1.2 Strichartz Estimates
1.1.3 Fourier Analysis and Self-similarity
1.1.4 Applications of Harmonic Analysis: Radon Transform, Wavelets, and Distributions
1.1.5 The Way of Analysis and the Guide to Distribution Theory and Fourier Transform
1.2 Analysis on Manifolds
1.2.1 Riemannian Geometry

1.2.2 Sub-Riemannian Geometry
1.2.3 Harmonic Analysis as Spectral Theory of Laplacians
1.3 Analysis on Fractals
1.3.1 Differential Equations on Fractals
1.3.2 Numerical Analysis on Fractals
1.3.3 Intrinsic Analysis on Fractafolds
1.4 Mentorship
References
Part II Functional and Harmonic Analysis on Euclidean Spaces
2 A New Proof of Strichartz Estimates for the Schrödinger Equation in 2+1 Dimensions
2.1 Introduction
2.2 Reduction to a Localized Bilinear Estimate
2.3 The Main Building Block
2.4 Proof of the Main Theorem
References
Untitled

6 Product Manifolds with Improved Spectral Cluster and Weyl Remainder Estimates
6.1 Introduction
6.2 Proof of Lq-Improvements and Some Applications
6.2.1 Some Applications
6.3 Improved Weyl Formulae
6.4 Further Results and Remarks
References
7 A Scalar-Valued Fourier Transform for the Heisenberg Group
7.1 Introduction
7.2 Fourier Transforms on the Heisenberg Group
7.2.1 Schrödinger Representations and the Group Fourier Transform
7.2.2 Joint Spectral Theory of L and T
7.2.3 Heisenberg Motion Group and Some Class One Representations