Fourier Integrals in Classical Analysis

Author: Christopher D. Sogge

Publisher: Cambridge University Press

ISBN: 9780521434645

Category: Mathematics

Page: 236

View: 477

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An advanced monograph concerned with modern treatments of central problems in harmonic analysis.

Classical Fourier Analysis

Author: Loukas Grafakos

Publisher: Springer

ISBN: 1493911945

Category: Mathematics

Page: 638

View: 3103

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The main goal of this text is to present the theoretical foundation of the field of Fourier analysis on Euclidean spaces. It covers classical topics such as interpolation, Fourier series, the Fourier transform, maximal functions, singular integrals, and Littlewood–Paley theory. The primary readership is intended to be graduate students in mathematics with the prerequisite including satisfactory completion of courses in real and complex variables. The coverage of topics and exposition style are designed to leave no gaps in understanding and stimulate further study. This third edition includes new Sections 3.5, 4.4, 4.5 as well as a new chapter on “Weighted Inequalities,” which has been moved from GTM 250, 2nd Edition. Appendices I and B.9 are also new to this edition. Countless corrections and improvements have been made to the material from the second edition. Additions and improvements include: more examples and applications, new and more relevant hints for the existing exercises, new exercises, and improved references.

Eigenfunctions of the Laplacian on a Riemannian Manifold

Author: Steve Zelditch

Publisher: American Mathematical Soc.

ISBN: 1470410370

Category: Eigenfunctions

Page: 394

View: 2304

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Eigenfunctions of the Laplacian of a Riemannian manifold can be described in terms of vibrating membranes as well as quantum energy eigenstates. This book is an introduction to both the local and global analysis of eigenfunctions. The local analysis of eigenfunctions pertains to the behavior of the eigenfunctions on wavelength scale balls. After re-scaling to a unit ball, the eigenfunctions resemble almost-harmonic functions. Global analysis refers to the use of wave equation methods to relate properties of eigenfunctions to properties of the geodesic flow. The emphasis is on the global methods and the use of Fourier integral operator methods to analyze norms and nodal sets of eigenfunctions. A somewhat unusual topic is the analytic continuation of eigenfunctions to Grauert tubes in the real analytic case, and the study of nodal sets in the complex domain. The book, which grew out of lectures given by the author at a CBMS conference in 2011, provides complete proofs of some model results, but more often it gives informal and intuitive explanations of proofs of fairly recent results. It conveys inter-related themes and results and offers an up-to-date comprehensive treatment of this important active area of research.

Classical and Modern Fourier Analysis

Author: Loukas Grafakos

Publisher: Prentice Hall

ISBN: N.A

Category: Mathematics

Page: 931

View: 7371

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For graduate-level courses in Fourier or harmonic analysis. Designed specifically for students (rather than researchers), this introduction to Fourier Analysis starts where the real and complex first-year graduate classes end.

Reports of the President and the Treasurer

Author: John Simon Guggenheim Memorial Foundation

Publisher: N.A

ISBN: N.A

Category: Scholarships

Page: N.A

View: 2069

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Includes: biographies of fellows appointed; reappointments; publications, musical compositions, academic appointments and index of fellows.