Spectral Riesz–Cesàro Means: How the Square Root Function Helps Us to See Around the World
نویسندگان
چکیده
The heat-kernel expansion for a nonanalytic function of a differential operator, and the integrated (Cesàro-smoothed) spectral densities associated with the corresponding nonanalytic function of the spectral parameter, exhibit a certain nonlocal behavior. Because of this phenomenon, care is needed in applying the pseudodifferential symbolic calculus to nonanalytic functions. We demonstrate this effect by both analytical and numerical calculations for the square root of the Laplace operator in the model of a “twisted” scalar field over the circle. This shows that the effect cannot be attributed solely to boundaries.
منابع مشابه
Divergent Cesàro and Riesz means of Jacobi and Laguerre expansions
We show that for δ below certain critical indices there are functions whose Jacobi or Laguerre expansions have almost everywhere divergent Cesàro and Riesz means of order δ.
متن کاملSome Properties of Riesz Means and Spectral Expansions
It is well known that short-time expansions of heat kernels correlate to formal high-frequency expansions of spectral densities. It is also well known that the latter expansions are generally not literally true beyond the first term. However, the terms in the heat-kernel expansion correspond rigorously to quantities called Riesz means of the spectral expansion, which damp out oscillations in th...
متن کاملMEMRI’s Narrative of Iran in the Context of Current US-Iran Tensions
Drawing on narrative theory and the notion of framing, this paper focused on the translated material from the Islamic Republic of Iran‟s media outlets in the website of the Middle East Media Research Institute (MEMRI) to explore how this institute constructed its desired narratives about Iran in the context of the current tensions between Iran and the U.S. In so ...
متن کاملWaves of Perception
We experience the world around us as “continuous,” which means everything around us seems uninterrupted and ongoing. But how does our brain achieve that? Here, we suggest that the brain samples our environment in separate snapshots. We demonstrate that brain waves work just like a flipbook, where the rapid stream of related pictures creates the illusion of a continuous movie. We present results...
متن کاملTraditional medicine and intellectual property
Medical plants have a great value in traditional knowledge related to human health care both used whole plant or consisting in curative remedies. These valuable uses has been led to commercial use of medicinal plants and their derivatives which makes great benefits. Also there is a growing desire to use of completely natural materials as curative drugs around the world. These facts show up a gr...
متن کامل