Skip to main content
We gratefully acknowledge support from the Simons Foundation, member institutions, and all contributors. Donate
arXiv logo
Cornell University Logo

Mathematics > Analysis of PDEs

arXiv:1811.10428 (math)
[Submitted on 26 Nov 2018 (v1), last revised 31 Dec 2021 (this version, v6)]

Title:Semiclassical Defect Measures and Observability Estimate for Schrödinger Operators with Homogeneous Potentials of Order Zero

Authors:Keita Mikami
View PDF
Abstract:We study the asymptotic behavior as |x| \to \infty of Schrödinger operators with homogeneous potentials. For this purpose, we use methods from semiclassical analysis and investigate semiclassical defect mesures. We prove their localization in direction which we apply in order to obtain a necessary condition of observability.
Comments: 24 pages. We improved the statement of the main theorem. We also fixed some mistakes
Subjects: Analysis of PDEs (math.AP); Mathematical Physics (math-ph); Spectral Theory (math.SP)
Cite as: arXiv:1811.10428 [math.AP]
  (or arXiv:1811.10428v6 [math.AP] for this version)
  https://doi.org/10.48550/arXiv.1811.10428

Submission history

From: Keita Mikami [view email]
[v1] Mon, 26 Nov 2018 14:57:14 UTC (14 KB)
[v2] Thu, 13 Dec 2018 13:25:41 UTC (14 KB)
[v3] Tue, 19 May 2020 05:56:00 UTC (14 KB)
[v4] Wed, 20 May 2020 16:53:35 UTC (14 KB)
[v5] Sun, 11 Oct 2020 16:25:39 UTC (14 KB)
[v6] Fri, 31 Dec 2021 14:00:59 UTC (17 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.AP
< prev   |   next >
new | recent | 2018-11
Change to browse by:
math
math-ph
math.MP
math.SP

References & Citations

export BibTeX citation

Bookmark

BibSonomy logo Reddit logo

Bibliographic and Citation Tools

Bibliographic Explorer (What is the Explorer?)
Connected Papers (What is Connected Papers?)
Litmaps (What is Litmaps?)
scite Smart Citations (What are Smart Citations?)

Code, Data and Media Associated with this Article

alphaXiv (What is alphaXiv?)
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub (What is DagsHub?)
Gotit.pub (What is GotitPub?)
Hugging Face (What is Huggingface?)
Papers with Code (What is Papers with Code?)
ScienceCast (What is ScienceCast?)

Demos

Replicate (What is Replicate?)
Hugging Face Spaces (What is Spaces?)
TXYZ.AI (What is TXYZ.AI?)

Recommenders and Search Tools

Influence Flower (What are Influence Flowers?)
CORE Recommender (What is CORE?)

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.

Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)