Classical and Multilinear Harmonic Analysis: Volume 1
eBook - PDF

Classical and Multilinear Harmonic Analysis: Volume 1

  1. English
  2. PDF
  3. Available on iOS & Android
eBook - PDF

Classical and Multilinear Harmonic Analysis: Volume 1

About this book

This two-volume text in harmonic analysis introduces a wealth of analytical results and techniques. It is largely self-contained and will be useful to graduate students and researchers in both pure and applied analysis. Numerous exercises and problems make the text suitable for self-study and the classroom alike. This first volume starts with classical one-dimensional topics: Fourier series; harmonic functions; Hilbert transform. Then the higher-dimensional Calderón–Zygmund and Littlewood–Paley theories are developed. Probabilistic methods and their applications are discussed, as are applications of harmonic analysis to partial differential equations. The volume concludes with an introduction to the Weyl calculus. The second volume goes beyond the classical to the highly contemporary and focuses on multilinear aspects of harmonic analysis: the bilinear Hilbert transform; Coifman–Meyer theory; Carleson's resolution of the Lusin conjecture; Calderón's commutators and the Cauchy integral on Lipschitz curves. The material in this volume has not previously appeared together in book form.

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Yes, you can access Classical and Multilinear Harmonic Analysis: Volume 1 by Camil Muscalu,Wilhelm Schlag in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematical Analysis. We have over one million books available in our catalogue for you to explore.

Table of contents

  1. Cover
  2. Series
  3. Title
  4. Copyright
  5. Contents
  6. Preface
  7. Acknowledgements
  8. 1 Fourier series: convergence and summability
  9. 2 Harmonic functions; Poisson kernel
  10. 3 Conjugate harmonic functions; Hilbert transform
  11. 4 The Fourier transform on R[sup(d)] and on LCA groups
  12. 5 Introduction to probability theory
  13. 6 Fourier series and randomness
  14. 7 Calderón–Zygmund theory of singular integrals
  15. 8 Littlewood–Paley theory
  16. 9 Almost orthogonality
  17. 10 The uncertainty principle
  18. 11 Fourier restriction and applications
  19. 12 Introduction to the Weyl calculus
  20. References
  21. Index