Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Linear Approximation in Frequency Domain01:26

Linear Approximation in Frequency Domain

136
Linear systems are characterized by two main properties: superposition and homogeneity. Superposition allows the response to multiple inputs to be the sum of the responses to each individual input. Homogeneity ensures that scaling an input by a scalar results in the response being scaled by the same scalar.
In contrast, nonlinear systems do not inherently possess these properties. However, for small deviations around an operating point, a nonlinear system can often be approximated as linear....
136
Linear Approximation in Time Domain01:21

Linear Approximation in Time Domain

128
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
128
Discrete-Time Fourier Series01:20

Discrete-Time Fourier Series

369
The Discrete-Time Fourier Series (DTFS) is a fundamental concept in signal processing, serving as the discrete-time counterpart to the continuous-time Fourier series. It allows for the representation and analysis of discrete-time periodic signals in terms of their frequency components. Unlike its continuous counterpart, which utilizes integrals, the calculation of DTFS expansion coefficients involves summations due to the discrete nature of the signal.
For a discrete-time periodic signal x[n]...
369
Determination of Expected Frequency01:08

Determination of Expected Frequency

2.3K
Suppose one wants to test independence between the two variables of a contingency table. The values in the table constitute the observed frequencies of the dataset. But how does one determine the expected frequency of the dataset? One of the important assumptions is that the two variables are independent, which means the variables do not influence each other. For independent variables, the statistical probability of any event involving both variables is calculated by multiplying the individual...
2.3K
Per-Unit Sequence Models01:26

Per-Unit Sequence Models

119
An ideal Y-Y transformer, grounded through neutral impedances, displays per-unit sequence networks akin to those of a single-phase ideal transformer when subjected to balanced positive- or negative-sequence currents. These currents do not produce neutral currents, and their associated voltage drops.
Zero-sequence currents, which are identical in magnitude and phase, generate a neutral current, resulting in voltage drops across the neutral impedance and the low-voltage winding. If the...
119
Parseval's Theorem for Fourier transform01:15

Parseval's Theorem for Fourier transform

1.3K
Parseval's theorem is a fundamental principle in signal processing that enables the calculation of a signal's energy in either the time domain or the frequency domain. This theorem is pivotal in demonstrating energy conservation between these two domains, ensuring that the computed energy value remains consistent regardless of the domain of analysis.
To understand Parseval's theorem, it is essential to first comprehend how signal energy is typically calculated. When considering a...
1.3K

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Prevalence of respiratory viruses in stable and acute asthma: a systematic review and meta-analysis.

European respiratory review : an official journal of the European Respiratory Society·2026
Same author

Exploring Aggressive Behaviors in Greek Secondary Schools: Prevalence, Sociodemographic Factors, and Comparative Analysis with Elementary School Students.

Behavioral sciences (Basel, Switzerland)·2024
Same author

Classification of anisotropic Triebel-Lizorkin spaces.

Mathematische annalen·2024
Same author

Prevalence and clinical implications of respiratory viruses in asthma during stable disease state and acute attacks: Protocol for a meta-analysis.

PloS one·2023
Same author

Incorporating Medical Museum Specimens Into the Training of Environmental Health Students.

Environmental health insights·2023
Same author

Prevalence of Aggressive Behavior in Greek Elementary School Settings from Teachers' Perspectives.

Behavioral sciences (Basel, Switzerland)·2023
Same journal

The nonlinear porous medium equation for the <i>f</i>-Laplacian: Hamilton-Souplet-Zhang type gradient estimates and implications.

Annali di matematica pura ed applicata·2026
Same journal

On the instability of syzygy bundles on toric surfaces.

Annali di matematica pura ed applicata·2026
Same journal

Partial regularity for minima of higher-order quasiconvex integrands with natural Orlicz growth.

Annali di matematica pura ed applicata·2025
Same journal

Optimal and typical <math></math> discrepancy of 2-dimensional lattices.

Annali di matematica pura ed applicata·2024
Same journal

Higher integrability for singular doubly nonlinear systems.

Annali di matematica pura ed applicata·2024
Same journal

A comparison principle for doubly nonlinear parabolic partial differential equations.

Annali di matematica pura ed applicata·2024
See all related articles

Related Experiment Video

Updated: Sep 15, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.6K

Counting function estimates for coherent frames and Riesz sequences.

Effie Papageorgiou1, Jordy Timo van Velthoven2

  • 1Institut für Mathematik, Universität Paderborn, Warburger Str. 100, D-33098 Paderborn, Germany.

Annali Di Matematica Pura Ed Applicata
|July 17, 2025
PubMed
Summary
This summary is machine-generated.

This study provides precise estimates for counting functions related to coherent frames and Riesz sequences. These findings establish density conditions for these mathematical structures on various groups.

Keywords:
Beurling densityCoherent systemCounting functionFrameRiesz sequence

More Related Videos

Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.1K
Observation and Analysis of Blinking Surface-enhanced Raman Scattering
05:52

Observation and Analysis of Blinking Surface-enhanced Raman Scattering

Published on: January 11, 2018

7.5K

Related Experiment Videos

Last Updated: Sep 15, 2025

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference
07:56

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

8.6K
Generation and Coherent Control of Pulsed Quantum Frequency Combs
06:42

Generation and Coherent Control of Pulsed Quantum Frequency Combs

Published on: June 8, 2018

9.1K
Observation and Analysis of Blinking Surface-enhanced Raman Scattering
05:52

Observation and Analysis of Blinking Surface-enhanced Raman Scattering

Published on: January 11, 2018

7.5K

Area of Science:

  • Harmonic Analysis
  • Functional Analysis
  • Group Theory

Background:

  • Coherent frames and Riesz sequences are fundamental structures in signal processing and mathematical analysis.
  • Understanding their density properties is crucial for applications and theoretical development.
  • Existing research provides foundational density conditions, but more precise estimates are needed.

Purpose of the Study:

  • To derive asymptotic estimates for counting functions associated with coherent frames and Riesz sequences.
  • To establish necessary density conditions for these structures on general unimodular amenable groups.
  • To refine these estimates for systems with additional localization properties on groups of polynomial growth.

Main Methods:

  • Asymptotic analysis of counting functions.
  • Techniques from harmonic analysis and group theory.
  • Exploration of localization properties within coherent systems.

Main Results:

  • New estimates for the asymptotics of counting functions related to coherent frames and Riesz sequences.
  • Recovery of known density conditions for these structures on unimodular amenable groups.
  • More precise asymptotic estimates for localized coherent systems on groups of polynomial growth.

Conclusions:

  • The study successfully establishes and refines density conditions for coherent frames and Riesz sequences.
  • The findings offer improved analytical tools for understanding these mathematical objects.
  • The results have implications for both the theoretical understanding and potential applications of frames and Riesz sequences.