Hermite function description of Feichtinger's space S0

A.J.E.M. Janssen

doi:10.1007/s00041-005-4077-y

Hermite function description of Feichtinger's space S0

A.J.E.M. Janssen

Control Systems

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Abstract

For ¿ ¿ R we let C(¿) be the set of all f ¿ S' for which ¿^infin;_n=0,|(f,h_n)|(n+1) ^¿ < 8, where (h_n)_n=0,1,... is the orthonormal base of Hermite functions. We show that C(¿) ¿ S ₀ if and only if ¿ = 1/4 and that S₀ ¿ C(¿) if and only if ¿ = 1/4. Here S₀ is Feichtinger's space.

Original language	English
Pages (from-to)	577-588
Number of pages	12
Journal	Journal of Fourier Analysis and Applications
Volume	11
Issue number	5
DOIs	https://doi.org/10.1007/s00041-005-4077-y
Publication status	Published - 2005

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title = "Hermite function description of Feichtinger's space S0",

abstract = "For ¿ ¿ R we let C(¿) be the set of all f ¿ S' for which ¿infin;n=0,|(f,hn)|(n+1) ¿ < 8, where (hn)n=0,1,... is the orthonormal base of Hermite functions. We show that C(¿) ¿ S 0 if and only if ¿ = 1/4 and that S0 ¿ C(¿) if and only if ¿ = 1/4. Here S0 is Feichtinger's space.",

author = "A.J.E.M. Janssen",

year = "2005",

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T1 - Hermite function description of Feichtinger's space S0

AU - Janssen, A.J.E.M.

PY - 2005

Y1 - 2005

N2 - For ¿ ¿ R we let C(¿) be the set of all f ¿ S' for which ¿infin;n=0,|(f,hn)|(n+1) ¿ < 8, where (hn)n=0,1,... is the orthonormal base of Hermite functions. We show that C(¿) ¿ S 0 if and only if ¿ = 1/4 and that S0 ¿ C(¿) if and only if ¿ = 1/4. Here S0 is Feichtinger's space.

AB - For ¿ ¿ R we let C(¿) be the set of all f ¿ S' for which ¿infin;n=0,|(f,hn)|(n+1) ¿ < 8, where (hn)n=0,1,... is the orthonormal base of Hermite functions. We show that C(¿) ¿ S 0 if and only if ¿ = 1/4 and that S0 ¿ C(¿) if and only if ¿ = 1/4. Here S0 is Feichtinger's space.

U2 - 10.1007/s00041-005-4077-y

DO - 10.1007/s00041-005-4077-y

M3 - Article

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VL - 11

SP - 577

EP - 588

JO - Journal of Fourier Analysis and Applications

JF - Journal of Fourier Analysis and Applications

IS - 5

ER -

Hermite function description of Feichtinger's space S0

Abstract

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