Corpus ID: 44194028

# Wavelet decomposition and bandwidth of functions defined on vector spaces over finite fields

@inproceedings{Iosevich2016WaveletDA,
title={Wavelet decomposition and bandwidth of functions defined on vector spaces over finite fields},
author={Alex Iosevich and Allen Qiankun Liu and Azita Mayeli and Jonathan Pakianathan},
year={2016}
}
• Alex Iosevich, +1 author Jonathan Pakianathan
• Published 2016
• Mathematics
• In this paper we study how zeros of the Fourier transform of a function $f: \mathbb{Z}_p^d \to \mathbb{C}$ are related to the structure of the function itself. In particular, we introduce a notion of bandwidth of such functions and discuss its connection with the decomposition of this function into wavelets. Connections of these concepts with the tomography principle and the Nyquist-Shannon sampling theorem are explored. We examine a variety of cases such as when the Fourier transform of the… CONTINUE READING

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#### References

##### Publications referenced by this paper.
SHOWING 1-7 OF 7 REFERENCES

## Certain Topics in Telegraph Transmission Theory

• Harry Nyquist
• Engineering
• Transactions of the American Institute of Electrical Engineers
• 2002

## Sampling-50 years after Shannon

VIEW 1 EXCERPT

## Multiresolution approximations and wavelet orthonormal bases of L^2(R)

VIEW 1 EXCERPT

## Orthonormal Bases of Compactly Supported Wavelets

VIEW 1 EXCERPT

## Decomposition of hardy functions into square integrable wavelets of constant shape

• Mathematics
• 1984
VIEW 1 EXCERPT

## et al

• C. Aten
• Tiling sets and spectral sets over finite fields, submitted for publication.
• 1090
VIEW 1 EXCERPT