A Kernel-Independent Sum-of-Gaussians Method by de la Vallee-Poussin Sums

2021 ◽  
Vol 13 (5) ◽  
pp. 1126-1141
Author(s):  
global sci
Keyword(s):  
De La Vallée Poussin

scholarly journals Edge detection with trigonometric polynomial shearlets

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Kevin Schober ◽  
Jürgen Prestin ◽  
Serhii A. Stasyuk
Keyword(s):  
Edge Detection ◽  
Trigonometric Polynomial ◽  
Two Dimensions ◽  
Characteristic Functions ◽  
Numerical Examples ◽  
Special Cases ◽  
Periodic Characteristic ◽  
Boundary Curves ◽  
Theoretical Results ◽  
De La Vallée Poussin

AbstractIn this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

The Fréchet Variation, Sector Limits, and Left Decompositions

1950 ◽  
Vol 2 ◽  
pp. 344-374 ◽  
Author(s):  
Marston Morse ◽  
William Transue
Keyword(s):  
Fourier Series ◽  
Variational Analysis ◽  
Cartesian Product ◽  
Multiple Fourier Series ◽  
Linear Spaces ◽  
Normed Linear Spaces ◽  
Variation Of A Function ◽  
De La Vallée Poussin

1. Introduction. The Fréchet variation of a function g defined over a 2-interval I2 was introduced by Fréchet to enable him to generalize Riesz's theorem on the representation of functionals linear over the space C [7]. Recently the authors have found this variation fundamental in the study of functionals bilinear over the Cartesian product A ⨯ B of two normed linear spaces with certain characteristic properties, and in the further use of this theory in spectral and variational analysis. The recent discovery by the authors of several new properties of the Fréchet variation has made it possible to to give new and natural tests for the convergence of multiple Fourier series generalizing the classical Jordan, de la Vallée Poussin, Dini, Young and Lebesgue tests under considerably less restrictive hypotheses than those now accepted.

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