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Everything about Weierstrass transform
"Smoothing" integral transform
In mathematics, the Weierstrass transform of a function, named after Karl Weierstrass, is a "smoothed" version of obtained by averaging the values of, weighted with a Gaussian centered at. Wikipedia â
đ§ Start here: a 6-step reading path
- Read the overview: Weierstrass transformA 5-minute orientation
- Skim a recent paper: Tikhonov regularisation for the Weierstrass transform associated with the KontorovichâLebedev transformInfluential work since 2022
- Pick up a classic book: Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical TablesThe most-reprinted book on the subject
- Read the landmark paper: The weierstrass transform and an isometry in the heat equationCited 67 times
- Go sideways: Hermite polynomialsA closely related topic
- Go sideways: Gaussian functionA closely related topic
đ Definitions
No dictionary entry for this exact phrase.
đïž The subject at a glance
đ Landmark papers (most cited)
The weierstrass transform and an isometry in the heat equation
Reconstructing Folding Energy Landscape Profiles from Nonequilibrium Pulling Curves with an Inverse Weierstrass Integral Transform
The Weierstrass Hankel convolution transform
Necessary and sufficient conditions for the representation of a function by a Weierstrass transform
The Weierstrass transform and Hermite polynomials
FourierâMukai transform on Weierstrass cubics and commuting differential operators
The Weierstrass-Laguerre transform
The dual Weierstrass-Laguerre transform
đ Influential since 2022
Tikhonov regularisation for the Weierstrass transform associated with the KontorovichâLebedev transform
Abelian Theorems for the Real Weierstrass Transform over Compactly Supported Distributions
Recognition Of Chicken Species Through Sound Using Weierstrass Transform
Mellin Transform of Weierstrass Zeta Function and Integral Representations of Some Lambert Series
Discrete Weierstrass Transform: Generalisations
đ Books worth reading
- đHandbook of Mathematical Functions, with Formulas, Graphs, and Mathematical TablesMilton Abramowitz · 1972
Fourier analysisElias M. Stein · 2003
Elements of the theory of elliptic and associated functions with applicationsMahadev Dutta, Lokenath Debnath · 1965
Calculus of Variations IIMariano Giaquinta · 2004
Calculus of Variations IMariano Giaquinta · 2004
An introduction to multivariable mathematicsSimon, L. · 2008
Methods for finding Zeros in PolynomialsLeif Mejlbro · 2013
Methods for finding Zeros in PolynomialsLeif Mejlbro · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
đ Related topics
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- Gaussian function In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f(x)=expâĄ(âx2) and with parametric extensionâŠ
- Gaussian integral The Gaussian integral, also known as the EulerâPoisson integral, is the integral of the Gaussian function over the entire real line. Named after the GermanâŠ
- Fourier transform In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extentâŠ
- Completing the square In elementary algebra, completing the square is a technique for converting a quadratic polynomial of the form â ax2+bx+câ to the form â a(xâh)2+kâ for someâŠ
- GaussâHermite quadrature In numerical analysis, GaussâHermite quadrature is a form of Gaussian quadrature for approximating the value of integrals of the following kind: â« â ââŠ
- Laplace operator In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a scalar function on EuclideanâŠ
- List of eponyms of special functions This is a list of special function eponyms in mathematics, to cover the theory of special functions, the differential equations they satisfy, named differentialâŠ