On the Gibbs–Wilbraham Phenomenon for Sampling and Interpolatory Series

Abstract

The Gibbs-Wilbraham phenomenon for generalized sampling series, and related interpolation series arising from cardinal functions is investigated. We prove existence of the overshoot characteristic of the phenomenon for certain cardinal functions, and characterize existence of an overshoot for sampling series.2010 Mathematics Subject Classification. 41A05,41A30,42C15.

On the Whitney near extension problem, BMO, alignment of data, best approximation in algebraic geometry, manifold learning and their beautiful connections: A modern treatment

“…The work of [54,94,58] provide a good overview of this subject. See also [118,115,114,117,1,99,59,116], [127,128,129,125,126,123,123,128,124,129], [104,105,103,18,109], [2,78,72,73,74,75,110,111], [11,25,71,82,85,86,87,116,135], [53,45,47,48,44,133], [90,…”

“…Regarding the shape matching and visual recognition problem in line with the discussions in Section (2) and Problem (7) in Section (2.3.3), we list the following references related to our work which provide a good overview, see [23,26,33,57,28,32], [118,115,114,117,1,99,59,116], [127,128,129,125,126,123,123,128,124,129], [104,105,103,18,109], [2,78,72,73,74,75,110,111], [11,25,71,82,85,86,87,116,135], [53,…”

“…Some classical non-linear manifold learning algorithms include Isomap [120], local linear embedding [108], Laplacian eigenmaps, [9], diffusions maps [26,27] and local linear embeddingvia Hessians [57]. See also [56,57,100,79], [118,115,114,117,1,99,59,116], [127,128,129,125,126,123,123,128,124,129], [104,105,103,18,109], [2,78,72,73,74,75,110,111], [11,25,71,82,85,86,87,116,…”