scholarly journals Weak regularity and finitely forcible graph limits

2018 ◽  
Vol 370 (6) ◽  
pp. 3833-3864 ◽  
Author(s):  
Jacob W. Cooper ◽  
Tomáš Kaiser ◽  
Daniel Král’ ◽  
Jonathan A. Noel
Keyword(s):  
Weak Regularity ◽  
Graph Limits

scholarly journals Weak regularity and finitely forcible graph limits

2015 ◽  
Vol 49 ◽  
pp. 139-143
Author(s):  
Jacob W. Cooper ◽  
Tomáš Kaiser ◽  
Daniel Král' ◽  
Jonathan A. Noel
Keyword(s):  
Weak Regularity ◽  
Graph Limits

L 1 and L ∞ stability of transition densities of perturbed diffusions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ilya Bitter ◽  
Valentin Konakov
Keyword(s):  
Linear Growth ◽  
Stability Result ◽  
Regularity Conditions ◽  
Initial Condition ◽  
Weak Regularity ◽  
Transition Densities ◽  
The Stability ◽  
Drift Terms

Abstract In this paper, we derive a stability result for L 1 {L_{1}} and L ∞ {L_{\infty}} perturbations of diffusions under weak regularity conditions on the coefficients. In particular, the drift terms we consider can be unbounded with at most linear growth, and the estimates reflect the transport of the initial condition by the unbounded drift through the corresponding flow. Our approach is based on the study of the distance in L 1 {L_{1}} - L 1 {L_{1}} metric between the transition densities of a given diffusion and the perturbed one using the McKean–Singer parametrix expansion. In the second part, we generalize the well-known result on the stability of diffusions with bounded coefficients to the case of at most linearly growing drift.

scholarly journals Reverse mathematics and a Ramsey-type König's Lemma

2012 ◽  
Vol 77 (4) ◽  
pp. 1272-1280 ◽  
Author(s):  
Stephen Flood
Keyword(s):  
Reverse Mathematics ◽  
Ramsey's Theorem ◽  
Weak Regularity ◽  
Ramsey’S Theorem ◽  
Ramsey Type ◽  
Weak König’S Lemma ◽  
König’S Lemma

AbstractIn this paper, we propose a weak regularity principle which is similar to both weak König's lemma and Ramsey's theorem. We begin by studying the computational strength of this principle in the context of reverse mathematics. We then analyze different ways of generalizing this principle.

scholarly journals The Feichtinger Conjecture for Wavelet Frames, Gabor Frames and Frames of Translates

2006 ◽  
Vol 58 (6) ◽  
pp. 1121-1143 ◽  
Author(s):  
Marcin Bownik ◽  
Darrin Speegle
Keyword(s):  
Regularity Condition ◽  
Finite Union ◽  
Gabor Frame ◽  
Gabor Frames ◽  
Wavelet Frame ◽  
Wavelet Frames ◽  
Wavelet System ◽  
Weak Regularity

AbstractThe Feichtinger conjecture is considered for three special families of frames. It is shown that if a wavelet frame satisfies a certain weak regularity condition, then it can be written as the finite union of Riesz basic sequences each of which is a wavelet system. Moreover, the above is not true for general wavelet frames. It is also shown that a sup-adjoint Gabor frame can be written as the finite union of Riesz basic sequences. Finally, we show how existing techniques can be applied to determine whether frames of translates can be written as the finite union of Riesz basic sequences. We end by giving an example of a frame of translates such that any Riesz basic subsequence must consist of highly irregular translates.

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