Christopher D. Sogge's Books

Hangzhou Lectures on Eigenfunctions of the Laplacian

By: Christopher D. Sogge

Write a review Read reviews Take a Quiz Solve Book Puzzle

Hangzhou Lectures on Eigenfunctions of the Laplacian

By: Christopher D. Sogge

Based on lectures given at Zhejiang University in Hangzhou, China, and Johns Hopkins University, this book introduces eigenfunctions on Riemannian manifolds. Christopher Sogge gives a proof of the sharp Weyl formula for the distribution of eigenvalues of Laplace-Beltrami operators, as well as an improved version of the Weyl formula, the Duistermaat-Guillemin theorem under natural assumptions on the geodesic flow. Sogge shows that there is quantum ergodicity of eigenfunctions if the geodesic flow is ergodic. Sogge begins with a treatment of the Hadamard parametrix before proving the first main result, the sharp Weyl formula. He avoids the use of Tauberian estimates and instead relies on sup-norm estimates for eigenfunctions. The author also gives a rapid introduction to the stationary phase and the basics of the theory of pseudodifferential operators and microlocal analysis. These are used to prove the Duistermaat-Guillemin theorem. Turning to the related topic of quantum ergodicity, Sogge demonstrates that if the long-term geodesic flow is uniformly distributed, most eigenfunctions exhibit a similar behavior, in the sense that their mass becomes equidistributed as their frequencies go to infinity.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

205

Publisher

Princeton University Press

Published Date

ISBN 10

0691160783

ISBN 13

9780691160788

Fourier Integrals in Classical Analysis

By: Christopher D. Sogge

Write a review Read reviews Take a Quiz Solve Book Puzzle

Fourier Integrals in Classical Analysis

By: Christopher D. Sogge

This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat–Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

349

Publisher

Cambridge University Press

Published Date

ISBN 10

110823433X

ISBN 13

9781108234337

Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

By: Christopher D. Sogge

Write a review Read reviews Take a Quiz Solve Book Puzzle

Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

By: Christopher D. Sogge

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

206

Publisher

Princeton University Press

Published Date

ISBN 10

1400850541

ISBN 13

9781400850549

Fourier Integrals in Classical Analysis

By: Christopher D. Sogge

Write a review Read reviews Take a Quiz Solve Book Puzzle

Fourier Integrals in Classical Analysis

By: Christopher D. Sogge

This advanced monograph is concerned with modern treatments of central problems in harmonic analysis. The main theme of the book is the interplay between ideas used to study the propagation of singularities for the wave equation and their counterparts in classical analysis. In particular, the author uses microlocal analysis to study problems involving maximal functions and Riesz means using the so-called half-wave operator. To keep the treatment self-contained, the author begins with a rapid review of Fourier analysis and also develops the necessary tools from microlocal analysis. This second edition includes two new chapters. The first presents Hörmander's propagation of singularities theorem and uses this to prove the Duistermaat-Guillemin theorem. The second concerns newer results related to the Kakeya conjecture, including the maximal Kakeya estimates obtained by Bourgain and Wolff.

Average ratings

N/A

Write a review

Solve jigsaw puzzle

Age

Page Count

349

Publisher

Cambridge University Press

Published Date

ISBN 10

1107120071

ISBN 13

9781107120075

Book's by Christopher D. Sogge

Hangzhou Lectures on Eigenfunctions of the Laplacian

Hangzhou Lectures on Eigenfunctions of the Laplacian

Fourier Integrals in Classical Analysis

Fourier Integrals in Classical Analysis

Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Hangzhou Lectures on Eigenfunctions of the Laplacian (AM-188)

Fourier Integrals in Classical Analysis

Fourier Integrals in Classical Analysis

Username

Password

Username

Password

Password again

Birthday

Email