Unbounded growth of band-limited functions
Lloyd N. Trefethen
TL;DR
This paper demonstrates that band-limited functions, which are bounded by 1 on negative x, can grow arbitrarily fast on positive x, revealing unexpected growth behavior.
Contribution
It introduces a new understanding of the growth potential of band-limited functions beyond traditional bounds.
Findings
Band-limited functions can grow arbitrarily fast on positive x
Growth behavior is unbounded despite boundedness on negative x
Challenges assumptions about growth limits of band-limited functions
Abstract
It is shown that a band-limited function bounded by 1 for negative x can grow arbitrarily fast for positive x.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMeromorphic and Entire Functions · Mathematical Dynamics and Fractals