Everything about Prolate spheroidal wave function

🧭 Start here: a 6-step reading path

1. Read the overview: Prolate spheroidal wave functionA 5-minute orientation
2. Skim a recent paper: Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functionsInfluential work since 2022
3. Pick up a classic book: Prolate Spheroidal Wave Functions of Order ZeroThe most-reprinted book on the subject
4. Read the landmark paper: Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - ICited 1,868 times
5. Go sideways: Oblate spheroidal wave functionA closely related topic
6. Go sideways: Almost contact manifoldA closely related topic

🏆 Landmark papers (most cited)

• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - I

  D. Slepian, H. O. Pollak · 1961 · Bell System Technical Journal · 1,868 citations

• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - II

  H. J. Landau, H. O. Pollak · 1961 · Bell System Technical Journal · 785 citations

• Prolate Spheroidal Wave Functions, Fourier Analysis and Uncertainty - IV: Extensions to Many Dimensions; Generalized Prolate Spheroidal Functions

  David Slepian · 1964 · Bell System Technical Journal · 638 citations

• Some Asymptotic Expansions for Prolate Spheroidal Wave Functions

  David Slepian · 1965 · Journal of Mathematics and Physics · 200 citations

• Eigenvalues Associated with Prolate Spheroidal Wave Functions of Zero Order

  David Slepian and Estelle Sonnenblick · 1965 · Bell System Technical Journal · 108 citations

• Wavelets Based on Prolate Spheroidal Wave Functions

  Gilbert G. Walter, Xiaoping Shen · 2004 · Journal of Fourier Analysis and Applications · 55 citations

• Sampling With Prolate Spheroidal Wave Functions

  Gilbert G. Walter, Xiaoping A. Shen · 2003 · Sampling Theory in Signal and Image Processing · 50 citations

• Analysis of spectral approximations using prolate spheroidal wave functions

  Li-Lian Wang · 2009 · Mathematics of Computation · 36 citations

🆕 Influential since 2022

• Reconstruction from the Fourier transform on the ball via prolate spheroidal wave functions

  Mikhail Isaev, Roman G. Novikov · 2022 · Journal de Mathématiques Pures et Appliquées · 11 citations

• Numerical reconstruction from the Fourier transform on the ball using prolate spheroidal wave functions

  Mikhail Isaev, Roman G Novikov, Grigory V Sabinin · 2022 · Inverse Problems · 10 citations

• Sound Field Reconstruction Using Prolate Spheroidal Wave Functions and Sparse Regularization

  Xuxin Zhang, Jingjun Lou, Shijian Zhu · 2023 · Sensors · 7 citations

• Numerical realization of diffuse sound pressure fields using prolate spheroidal wave functions

  Cédric Van hoorickx, Edwin P. B. Reynders · 2022 · The Journal of the Acoustical Society of America · 7 citations

• Efficient realization of on-demand functional ultrasonic fields based on prolate spheroidal wave functions from sampling theorem

  Ya-Xi Shen, Xue-Feng Zhu · 2022 · The Journal of the Acoustical Society of America · 5 citations

📚 Books worth reading

• Prolate Spheroidal Wave Functions of Order ZeroAndrei Osipov, Vladimir Rokhlin · 2013
• Prolate spheroidal wave functions for electromagnetic theoryWalter L. Weeks · 1959
• Prolate Spheroidal Wave Functions of Order Zero Applied Mathematical SciencesAndrei Osipov · 2013
• 📕Tables of angular spheroidal wave functionsA. L. Van Buren · 1975
• 📕Tables of radial spheroidal functionsS. Hanish · 1970
• 📕Tables of spheriodal wave functionsS. Hanish · 1966
• Awareness Techniques by William SwygardWilliam Swygard · 1971

Ranked by number of editions on Open Library, a rough measure of how lasting a book is.

🔗 Related topics

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