Synapse
⌘+K
Synapse
PulseExploreClubsResearchersJournals
Instagram
HomeClubsExplore
March 3, 2026Open Access

An Eigenvector Problem Arising in the Study of Convergence of Walsh–Fourier Series

View Full Paper
Ask AI
Bookmark
Share

Authors

JHJeffrey A. HoganJLJoseph D. Lakey

Discussion

Loading...

Member takes

Overview

This work establishes eigenvalue bounds for truncated matrices in Walsh-Fourier series, suggesting new convergence methods.

Key Points

  • This research aims to establish bounds for specific matrices related to the convergence of Walsh-Fourier series.
  • Analyzed truncated matrices derived from orthogonal matrices for expansions in Walsh functions.
  • Investigated truncation operations on orthogonal matrices corresponding to dyadic step functions.
  • Demonstrated interplay between continuous and discrete sets to derive results.
  • Provided an approximate eigenvalue bound indicating convergence behavior of truncation norms.
  • Showed that truncation norms approach a fixed value as matrix dimensions increase.
  • Confirmed that integer samples of certain sinusoidal functions act as approximate eigenvectors.

Cite This Study

Hogan et al. (2026) studied this question.

synapsesocial.com/papers/69a67eebf353c071a6f0a958https://doi.org/10.3390/math14050829
View Full Paper
Ask AI
Bookmark
Share

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Convergence of matrix transform means with respect to the Walsh–Kaczmarz system2024 · 1 citations
  2. 2Approximation of double Walsh–Fourier series by means of the matrix transform2024
  3. 3Spectral norm bound for the product of random Fourier-Walsh matrices2025
  4. 4Eigenvalue estimates for Fourier concentration operators on two domains2024 · 9 citations
  5. 5Unconditional convergence of eigenfunction expansions for abstract and elliptic operators2024 · 4 citations