Titlebook: Geodesic Beams in Eigenfunction Analysis; Yaiza Canzani,Jeffrey Galkowski Book 2023 The Editor(s) (if applicable) and The Author(s), under

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Book 2023ce of mathematicians. Readers will gain an introduction to geodesic beams and the modern theory of Laplace eigenfunctions, which will enable them to understand the cutting edge aspects of this theory..

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報(bào)復(fù)

,The Koch–Tataru–Zworski Approach to?, Estimates, equivalent to . microlocally near .?[Zwo12, Theorem 12.3]. The crucial point in the approach from?[KTZ07] is that one need only make a physical change of variables to reduce to a first order hyperbolic operator. The main aim of this chapter is to prove the standard H?rmander . estimate using the Koch-Tataru-Zworski method.

insincerity

Book 2023roduction to the theory of Laplace eigenfunctions followed by an accessible treatment of geodesic beams and their applications to sup norm estimates, L^p estimates,? averages,?and Weyl laws.? Geodesic beams have proven to be a valuable tool in the study of Laplace eigenfunctions, but their treatment

GUEER

The Laplace Operator, in mathematics. We then recall the state of the art estimates on a variety of quantities involving high energy eigenfunctions. The bulk of this book will be devoted to the proof of many of these estimates.

GUEER

Lignans

,The Koch–Tataru–Zworski Approach to?, Estimates,. on . is microlocally equivalent to a first order hyperbolic operator along the direction of the Hamiltonian flow. Here, . is the canonical projection. Indeed, it is well known that if . on ., then under a ‘microlocal change of variables’, i.e. after conjugation by a Fourier integral operator, . is

Expressly

Dynamical Ideas,n Theorems?. and?.. For the details of the proofs, we refer the readers to?[CG20b] and?[CG19a]. Although the ideas remain the same, because one looks for quantitative information about sets undergoing the geodesic flow for large times, the precise proofs become substantially more complicated.

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