Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Hardy Spaces
  • Cited by 21
Publisher:
Cambridge University Press
Online publication date:
January 2019
Print publication year:
2019
Online ISBN:
9781316882108
DOI:
https://doi.org/10.1017/9781316882108
Subjects:
Mathematics (general), Mathematics, Abstract Analysis, Real and Complex Analysis
Series:
Cambridge Studies in Advanced Mathematics (179)
Information

Book description

The theory of Hardy spaces is a cornerstone of modern analysis. It combines techniques from functional analysis, the theory of analytic functions and Lesbesgue integration to create a powerful tool for many applications, pure and applied, from signal processing and Fourier analysis to maximum modulus principles and the Riemann zeta function. This book, aimed at beginning graduate students, introduces and develops the classical results on Hardy spaces and applies them to fundamental concrete problems in analysis. The results are illustrated with numerous solved exercises that also introduce subsidiary topics and recent developments. The reader's understanding of the current state of the field, as well as its history, are further aided by engaging accounts of important contributors and by the surveys of recent advances (with commented reference lists) that end each chapter. Such broad coverage makes this book the ideal source on Hardy spaces.

Reviews

'This is a beautiful introduction to a beautiful subject. The author does a masterful job of choosing topics that give a solid introduction to Hardy spaces without overwhelming the reader with too much too soon. Every student of mathematics should enjoy this book.'

John McCarthy - Washington University, St Louis

'This is an excellent, highly-recommendable book by a leading expert in the field. Describing in a self-contained way the classical approach to Hardy spaces and their applications - with emphasis on the invariant subspace point of view - it also offers an entertaining journey into the history of twentieth-century analysis.'

Joaquim Bruna - Universitat Autònoma de Barcelona

'The author has created a very interesting text that will serve as a source of basic material and an introduction for those interested in the interactions between harmonic analysis, complex analysis, and operator theory. Any researcher who masters the material in this text is well placed to read the more intensive monographs that further develop the interactions of these subjects.'

Brett Wick - Washington University, St Louis

'From the high stand due to a lifelong affinity for the subject, Nikolaï Nikolski delineates and recounts the fascinating history of Hardy space with style. His inviting text is sparkled with biographical snapshots, colorful anecdotes, and insightful remarks, conveying a vivid picture of the field. The mathematical discourse is light, yet rigorous and self-contained. Carefully selected problems offer the earnest reader perspectives into current research. The apogee chapter is devoted to the immersion of the daunting Riemann hypothesis into Hardy space framework … Nikolski’s text is a truly masterful piece of scholarship.'

Mihai Putinar - University of California, Santa Barbara

'This is a comfortably paced introduction to the theory of Hardy spaces, starting at a level of advanced graduate students in analysis … Historical context and biographical details of the main researchers of the field is discussed more deeply than in comparable books.'

M. Bona Source: Choice

‘To help the reader through this material, Nikolski is both an experienced educator and writer and knows how to present the material, efficiently … so the student can learn as well as appreciate the subject. Nikolski also gives us plenty of historical vignettes of the main figures in the development of Hardy spaces and, especially for the student, gives several appendices for those needing some gentle reminders of measure theory, complex analysis, Hilbert spaces, Banach spaces, and operator theory.’

William T. Ross Source: Bulletin of the American Mathematical Society

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Contents
References

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Book summary page views

Total views: 0 *
Loading metrics...

* Views captured on Cambridge Core between #date#. This data will be updated every 24 hours.

Usage data cannot currently be displayed.