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Everything about Slepian function
Mathematical function
Slepian functions are a class of spatio-spectrally concentrated functions that form an orthogonal basis for bandlimited or spacelimited spaces. That is, they are concentrated in space or time while spectrally bandlimited, or concentrated in spectral band while space- or time-limited. They are widely used as basis functions for constructive approximation and in linear inverse problems, and as apodization tapers or window functions in quadratic problems of spectral density estimation. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Slepian functionA 5-minute orientation
- Skim a recent paper: Inversion of GNSS Vertical Displacements for Terrestrial Water Storage Changes Using Slepian Basis FunctionsInfluential work since 2022
- Pick up a classic book: Lectures on Constructive ApproximationThe most-reprinted book on the subject
- Read the landmark paper: Spherical Slepian functions and the polar gap in geodesyCited 136 times
- Go sideways: Prolate spheroidal wave functionA closely related topic
- Go sideways: MultitaperA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🏆 Landmark papers (most cited)
Spherical Slepian functions and the polar gap in geodesy
Reconstructing Regional Ionospheric Electron Density: A Combined Spherical Slepian Function and Empirical Orthogonal Function Approach
On the Reliability Function of Variable-Rate Slepian-Wolf Coding
The analysis of gradiometric data with Slepian functions
Slepian Function-Based Windowed OFDM Systems With High Mobility
On Spectral Approximations by Generalized Slepian Functions
Vectorial Slepian Functions on the Ball
Variable altitude cognizant Slepian functions
🆕 Influential since 2022
Inversion of GNSS Vertical Displacements for Terrestrial Water Storage Changes Using Slepian Basis Functions
Recovering Ion Distribution Functions. I. Slepian Reconstruction of Velocity Distribution Functions from MMS and Solar Orbiter
Recovering Ion Distribution Functions. II. Gyrotropic Slepian Reconstruction of Solar Wind Electrostatic Analyzer Measurements
Recipe for Inferring Subsurface Solar Magnetism via Local Mode Coupling Using Slepian Basis Functions
A unified approach to scalar, vector, and tensor Slepian functions on the sphere and their construction by a commuting operator
📚 Books worth reading
Lectures on Constructive ApproximationVolker Michel · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- David Slepian David S. Slepian (June 30, 1923 – November 29, 2007) was an American mathematician. He is best known for his work with algebraic coding theory, probability…
- Henry O. Pollak Henry Otto Pollak (December 13, 1927 – July 8, 2026) was an Austrian-American mathematician who has made significant contributions to operator theory,…
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