scholarly journals Asymptotic singular value decay of time-frequency localization operators

1994 ◽  
Author(s):  
Christopher E. Heil ◽  
Jayakumar Ramanathan ◽  
Pankaj N. Topiwala
Keyword(s):  
Singular Value ◽  
Localization Operators ◽  
Time Frequency ◽  
Time Frequency Localization

Local Price uncertainty principle and time-frequency localization operators for the Hankel–Stockwell transform

2020 ◽  
Vol 18 (06) ◽  
pp. 2050050
Author(s):  
Nadia Ben Hamadi ◽  
Zineb Hafirassou
Keyword(s):  
Uncertainty Principle ◽  
Price Uncertainty ◽  
Localization Operators ◽  
Von Neumann ◽  
Time Frequency ◽  
Neumann Class ◽  
Time Frequency Localization ◽  
Stockwell Transform

For the Hankel–Stockwell transform, the Price uncertainty principle is proved, we define the Localization operators and we study their boundedness and compactness. We also show that these operators belong to the so-called Schatten–von Neumann class.

scholarly journals Sampling time-frequency localized functions and constructing localized time-frequency frames

2016 ◽  
Vol 28 (5) ◽  
pp. 854-876 ◽  
Author(s):  
G. A. M. VELASCO ◽  
M. DÖRFLER
Keyword(s):  
Region Of Interest ◽  
Main Tool ◽  
Sampling Time ◽  
Frequency Content ◽  
Gabor System ◽  
Localization Operators ◽  
Time Frequency ◽  
Compact Region ◽  
Time Frequency Localization ◽  
Finite Linear

We study functions whose time-frequency content are concentrated in a compact region in phase space using time-frequency localization operators as a main tool. We obtain approximation inequalities for such functions using a finite linear combination of eigenfunctions of these operators, as well as a local Gabor system covering the region of interest. These would allow the construction of modified time-frequency dictionaries concentrated in the region.

scholarly journals Subexponential decay and regularity estimates for eigenfunctions of localization operators

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Federico Bastianoni ◽  
Nenad Teofanov
Keyword(s):  
Pseudodifferential Operators ◽  
Modulation Space ◽  
Modulation Spaces ◽  
Weight Functions ◽  
Auxiliary Result ◽  
Localization Operators ◽  
Time Frequency ◽  
Continuity Properties ◽  
Regularity Properties ◽  
Time Frequency Localization

AbstractWe consider time-frequency localization operators $$A_a^{\varphi _1,\varphi _2}$$ A a φ 1 , φ 2 with symbols a in the wide weighted modulation space $$ M^\infty _{w}({\mathbb {R}^{2d}})$$ M w ∞ ( R 2 d ) , and windows $$ \varphi _1, \varphi _2 $$ φ 1 , φ 2 in the Gelfand–Shilov space $$\mathcal {S}^{\left( 1\right) }(\mathbb {R}^d)$$ S 1 ( R d ) . If the weights under consideration are of ultra-rapid growth, we prove that the eigenfunctions of $$A_a^{\varphi _1,\varphi _2}$$ A a φ 1 , φ 2 have appropriate subexponential decay in phase space, i.e. that they belong to the Gelfand–Shilov space $$ \mathcal {S}^{(\gamma )} (\mathbb {R^{d}}) $$ S ( γ ) ( R d ) , where the parameter $$\gamma \ge 1 $$ γ ≥ 1 is related to the growth of the considered weight. An important role is played by $$\tau $$ τ -pseudodifferential operators $$Op_{\tau } (\sigma )$$ O p τ ( σ ) . In that direction we show convenient continuity properties of $$Op_{\tau } (\sigma )$$ O p τ ( σ ) when acting on weighted modulation spaces. Furthermore, we prove subexponential decay and regularity properties of the eigenfunctions of $$Op_{\tau } (\sigma )$$ O p τ ( σ ) when the symbol $$\sigma $$ σ belongs to a modulation space with appropriately chosen weight functions. As an auxiliary result we also prove new convolution relations for (quasi-)Banach weighted modulation spaces.

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