NDLI: An Uncertainty Principle on Compact Manifolds

Content Provider	Springer Nature Link
Author	Steinerberger, Stefan
Copyright Year	2014
Abstract	Breitenberger’s uncertainty principle on the torus $$\mathbb {T}$$ and its higher-dimensional analogue on $$\mathbb {S}^{d-1}$$ are well understood. We describe an entire family of uncertainty principles on compact manifolds $$(M,g)$$ , which includes the classical Heisenberg–Weyl uncertainty principle (for $$M=B(0,1) \subset \mathbb {R}^d$$ the unit ball with the flat metric) and the Goh–Goodman uncertainty principle (for $$M=\mathbb {S}^{d-1}$$ with the canonical metric) as special cases. This raises a new geometric problem related to small-curvature low-distortion embeddings: given a function $$f:M \rightarrow \mathbb {R}$$ , which uncertainty principle in our family yields the best result? We give a (far from optimal) answer for the torus, discuss disconnected manifolds and state a variety of other open problems.
Ending Page	599
Page Count	25
Starting Page	575
File Format	PDF
ISSN	10695869
e-ISSN	15315851
Journal	Journal of Fourier Analysis and Applications
Issue Number	3
Volume Number	21
Language	English
Publisher	Springer US
Publisher Date	2014-12-25
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Abstract Harmonic Analysis Mathematical Methods in Physics Uncertainty principles Fourier Analysis Signal, Image and Speech Processing Compact manifolds Inequalities for sums, series and integrals Approximations and Expansions Analysis on homogeneous spaces Partial Differential Equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Analysis

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

An Uncertainty Principle and Sampling Inequalities in Besov Spaces

Eigenfunction expansions and the pinsky phenomenon on compact manifolds

Fourier Series on Compact Symmetric Spaces: K-Finite Functions of Small Support

The uncertainty principle: A mathematical survey

Almost Everywhere Convergent Fourier Series

Uncertainty Principles and Light Cones

Refined Sobolev Inequalities in Lorentz Spaces

Pointwise Fourier inversion on tori and other compact manifolds

Weak Uncertainty Principles on Fractals

An Uncertainty Principle on Compact Manifolds

Similar Documents

An Uncertainty Principle and Sampling Inequalities in Besov Spaces

Eigenfunction expansions and the pinsky phenomenon on compact manifolds

Fourier Series on Compact Symmetric Spaces: K-Finite Functions of Small Support

The uncertainty principle: A mathematical survey

Almost Everywhere Convergent Fourier Series

Uncertainty Principles and Light Cones

Refined Sobolev Inequalities in Lorentz Spaces

Pointwise Fourier inversion on tori and other compact manifolds

Weak Uncertainty Principles on Fractals

An Uncertainty Principle on Compact Manifolds