On the jump behavior of distributions and logarithmic averages
The jump behavior and symmetric jump behavior of distributions are studied. We give several formulas for the jump of distributions in terms of logarithmic averages, this is done in terms of Cesàro-logarithmic means of decompositions of the Fourier transform and in terms of logarithmic radial and angular local asymptotic behaviors of harmonic conjugate functions. Application to Fourier series are analyzed. In particular, we give formulas for jumps of periodic distributions in terms of Cesàro-Riesz logarithmic means and Abel-Poisson logarithmic means of conjugate Fourier series. © 2008 Elsevier Inc. All rights reserved.
Publication Source (Journal or Book title)
Journal of Mathematical Analysis and Applications
Vindas, J., & Estrada, R. (2008). On the jump behavior of distributions and logarithmic averages. Journal of Mathematical Analysis and Applications, 347 (2), 597-606. https://doi.org/10.1016/j.jmaa.2008.06.014