On pointwise convergence of schrödinger means
WebIn this paper, we investigate the probabilistic pointwise convergence problem of Schrödinger equation on the manifolds. We prove probabilistic pointwise convergence of the solutions to Schrödinger equations with the initial data in L 2 ( T n), where T = [ 0, 2 π), which require much less regularity for the initial data than the rough data case. Web16 de out. de 2024 · For functions in the Sobolev space Hs and decreasing sequences tn→0 we examine convergence almost everywhere of the generalized Schrödinger means …
On pointwise convergence of schrödinger means
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Web3 de mar. de 2024 · We consider Carleson's problem regarding pointwise convergence for the Schrödinger equation. Bourgain recently proved that there is initial data, in with , for … Web15 de out. de 2024 · Sjölin, P.: L p maximal estimates for solutions to the Schrödinger equation. Math. Scand., 81, 35–68 (1997) Article MathSciNet Google Scholar Sogge, C. D.: On the convergence of Riesz means on compact manifolds. Ann. of Math. (2), 126, 439–447 (1987) Article MathSciNet Google Scholar
WebFinally, we show the stochastic continuity of Schrödinger equation with random data in $\hat{L}^{r}(\mathbb{R}^n)(2\leq r<\infty)$ almost surely. The main ingredients are Lemmas 2.4, 2.5, 3.2-3.4. In this paper, we consider the convergence problem of … WebOur main theorem is a fractal $L^2$ restriction estimate, which also gives improved results on the size of the divergence set of the Schrödinger solutions, the Falconer distance set problem and the spherical average Fourier decay rates of fractal measures.
Web29 de jun. de 2024 · We consider the pointwise convergence problem for the solution of Schrödinger-type equations along directions determined by a given compact subset of the real line. This problem contains Carleson’s problem as the simplest case and was studied in general by Cho et al. Webadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A
Web9 de jun. de 2024 · On pointwise convergence of Schrödinger means. For functions in the Sobolev space and decreasing sequences we examine convergence almost …
Web1 de mar. de 2024 · Almost everywhere convergence on the solution of Schrödinger equation is an important problem raised by Carleson, which was essentially solved by Du … grant thornton crystal wealthWeb16 de jun. de 2024 · The goal of this note is to establish non-tangential convergence results for Schrödinger operators along restricted curves. We consider the relationship between the dimension of this kind of approach region and the regularity for the initial data which implies convergence. chip online originWeb4. Convergence using the Abel mean The issues surrounding the convergence of the Fourier series are not straight-forward. The Fourier series of a function integrable on [ ˇ;ˇ] does not converge pointwise to the function itself since the derivation of Fourier coe cients is done through integration. For example, consider this piecewise-de ned ... grant thornton cta.xWeb10 de set. de 2024 · We investigate the pointwise convergence of the solution to the fractional Schrödinger equation in . By establishing estimates for the associated maximal operator provided that , we improve the previous result obtained by Miao, Yang, and Zheng. grant thornton csrWebIt may help if you unfold the definition of limit in pointwise convergence. Then pointwise convergence means that for each x and ϵ you can find an N such that (bla bla bla). Here the N is allowed to depend both on x and ϵ. In uniform … chip online oster specialWebCorpus ID: 182952408; On pointwise convergence of Schr\"odinger means @article{Dimou2024OnPC, title={On pointwise convergence of Schr\"odinger means}, … chip online pdf24 creatorWeb14 de jul. de 2016 · Vega L.: Schrödinger equations: pointwise convergence to the initial data. Proc. Am. Math. Soc. 102(4), 874–878 (1988) MATH Google Scholar Yajima K.: Existence of solutions for Schrödinger evolution equations. Commun. Math. Phys. 110(3), 415–426 (1987) Article ADS MATH Google Scholar chip online opera download