Everything about Hankel transform
Mathematical operation
In mathematics, the Hankel transform expresses any given function f(r) as the weighted sum of an infinite number of Bessel functions of the first kind Jν(kr). The Bessel functions in the sum are all of the same order ν, but differ in a scaling factor k along the r axis. The necessary coefficient Fν of each Bessel function in the sum, as a function of the scaling factor k constitutes the transformed function. The Hankel transform is an integral transform and was first developed by the mathematician Hermann Hankel. It is also known as the Fourier–Bessel transform. Just as the Fourier transform for an infinite interval is related to the Fourier series over a finite interval, so the Hankel transform over an infinite interval is related to the Fourier–Bessel series over a finite interval. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Hankel transformA 5-minute orientation
- Skim a recent paper: Linear canonical deformed Hankel transform and the associated uncertainty principlesInfluential work since 2022
- Pick up a classic book: The distributional Hankel transformationThe most-reprinted book on the subject
- Read the landmark paper: Quasi fast Hankel transformCited 250 times
- Go sideways: Bessel functionA closely related topic
- Go sideways: Y and H transformsA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Quasi fast Hankel transform
Quasi-discrete Hankel transform
Fast Hankel transform algorithm
Bispectrum-window convolution via Hankel transform
The Weierstrass Hankel convolution transform
Uncertainty principles for the Hankel transform
Fast Hankel transform of nth order
On the Hankel transform of distributions
🆕 Influential since 2022
Linear canonical deformed Hankel transform and the associated uncertainty principles
Localization Operators and Scalogram Associated with the Deformed Hankel Wavelet Transform
Wavelet packets analysis for the deformed Hankel transform
Discrete fractional Hankel transform based on a nonsymmetric kernel matrix
Hankel-type Segal–Bargmann transform and its applications to UP and PDEs
📚 Books worth reading
- 📕The distributional Hankel transformationA. H. Zemanian · 1965
- 📕A Hankel convolution complex inversion theoryFrank M. Cholewinski · 1965
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
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