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

Mathematics > Complex Variables

arXiv:1007.5134 (math)
[Submitted on 29 Jul 2010 (v1), last revised 22 Oct 2010 (this version, v2)]

Title:Bounded Mean Oscillation and Bandlimited Interpolation in the Presence of Noise

Authors:Gaurav Thakur
View PDF
Abstract:We study some problems related to the effect of bounded, additive sample noise in the bandlimited interpolation given by the Whittaker-Shannon-Kotelnikov (WSK) sampling formula. We establish a generalized form of the WSK series that allows us to consider the bandlimited interpolation of any bounded sequence at the zeros of a sine-type function. The main result of the paper is that if the samples in this series consist of independent, uniformly distributed random variables, then the resulting bandlimited interpolation almost surely has a bounded global average. In this context, we also explore the related notion of a bandlimited function with bounded mean oscillation. We establish some properties of such functions, and in particular, we show that they are either bounded or have unbounded samples at any positive sampling rate. We also discuss a few concrete examples of functions that demonstrate these properties.
Subjects: Complex Variables (math.CV); Functional Analysis (math.FA)
MSC classes: Primary 30E05, Secondary 94A20, 30D15, 30H35
Cite as: arXiv:1007.5134 [math.CV]
  (or arXiv:1007.5134v2 [math.CV] for this version)
  https://doi.org/10.48550/arXiv.1007.5134
Journal reference: Journal of Functional Analysis 260(8):2283-2299, 2011
Related DOI: https://doi.org/10.1016/j.jfa.2010.10.015

Submission history

From: Gaurav Thakur [view email]
[v1] Thu, 29 Jul 2010 07:37:13 UTC (252 KB)
[v2] Fri, 22 Oct 2010 18:11:49 UTC (252 KB)
Full-text links:

Access Paper:

  • View PDF
  • TeX Source
  • Other Formats
view license
Current browse context:
math.CV
< prev   |   next >
new | recent | 2010-07
Change to browse by:
math
math.FA

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?)