Time frequency representations of almost periodic functions

Yeon Hyang Kim; Amos Ron

doi:10.1007/s00365-007-9000-0

Time frequency representations of almost periodic functions

Yeon Hyang Kim, Amos Ron

Research output: Contribution to journal › Article › peer-review

5 Scopus citations

Abstract

In this paper, we characterize the space of almost periodic (AP) functions in one variable using either a Weyl-Heisenberg (WH) system or an affine system. Our observation is that the sought-for characterization of the AP space is valid if and only if the given WH (respectively, affine) system is an L ₂(ℝ)-frame. Moreover, the frame bounds of the system are also the sharpest bounds in our characterization. This draws an intriguing and quite unexpected connection between L ₂(ℝ) representations and AP-representations.

Original language	English
Pages (from-to)	303-323
Number of pages	21
Journal	Constructive Approximation
Volume	29
Issue number	3
DOIs	https://doi.org/10.1007/s00365-007-9000-0
State	Published - Jun 2009
Externally published	Yes

Keywords

AP-frames
Affine systems
Almost-periodic functions
Dual Gramian
Fiberization of time frequency representations
Frames
Time frequency representations
Weyl-Heisenberg systems

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10.1007/s00365-007-9000-0

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abstract = "In this paper, we characterize the space of almost periodic (AP) functions in one variable using either a Weyl-Heisenberg (WH) system or an affine system. Our observation is that the sought-for characterization of the AP space is valid if and only if the given WH (respectively, affine) system is an L 2(ℝ)-frame. Moreover, the frame bounds of the system are also the sharpest bounds in our characterization. This draws an intriguing and quite unexpected connection between L 2(ℝ) representations and AP-representations.",

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AU - Ron, Amos

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AB - In this paper, we characterize the space of almost periodic (AP) functions in one variable using either a Weyl-Heisenberg (WH) system or an affine system. Our observation is that the sought-for characterization of the AP space is valid if and only if the given WH (respectively, affine) system is an L 2(ℝ)-frame. Moreover, the frame bounds of the system are also the sharpest bounds in our characterization. This draws an intriguing and quite unexpected connection between L 2(ℝ) representations and AP-representations.

KW - AP-frames

KW - Affine systems

KW - Almost-periodic functions

KW - Dual Gramian

KW - Fiberization of time frequency representations

KW - Frames

KW - Time frequency representations

KW - Weyl-Heisenberg systems

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VL - 29

SP - 303

EP - 323

JO - Constructive Approximation

JF - Constructive Approximation

IS - 3

ER -

Time frequency representations of almost periodic functions

Abstract

Keywords

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