A sampling theory for non-decaying signals in mixed Lebesgue spaces

Abstract

In this paper, we study the sampling theory for non-decaying signals in mixed Lebesgue spaces $L_{p,q}\left({\mathbb{R}}^{d+1}\right)$. First, we give some Riesz-type bounds, which connect the weighted discrete norms of the samples to the weighted continuous norms of original and interpolated signals. Then, we prove that the sampling and reconstruction through the Riesz-type bounds are stable when the generated kernel is in the appropriate mixed Wiener amalgam spaces.

COMMUNICATED BY:

• Zuhair Nashed

Keywords:

• Mixed Lebesgue spaces
• shift-invariant spaces
• sampling theory
• non-decaying signals
• submultiplicative weights

2010 MR Subject Classifications:

• 94A20
• 42C15
• 42C40

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported partially by the National Natural Science Foundation of China (Grant Numbers 11671214, 11971348), the Natural Science Foundation of Tianjin City  (Grant Number 18JCYBJC16200) and the Natural Science Research Project of Higher Education of Tianjin (Grant Number 2018KJ148).