The Hilbert transform is, without question, the most important operator in analysis. It arises in many different contexts, and all these contexts are intertwined in profound and influential ways. What it all comes down to is that there is only one singular integral in dimension 1, and it is the Hilbert transform. The philosophy is that all significant analytic questions reduce to a singular integral; and in the first dimension there is just one choice.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2009 Birkhäuser Boston, a part of Springer Science+Business Media, LLC
About this chapter
Cite this chapter
Krantz, S.G. (2009). The Central Idea: The Hilbert Transform. In: Explorations in Harmonic Analysis. Applied and Numerical Harmonic Analysis. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4669-1_2
Download citation
DOI: https://doi.org/10.1007/978-0-8176-4669-1_2
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-4668-4
Online ISBN: 978-0-8176-4669-1
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)