scholarly journals The Grossmann–Royer Transform, Gelfand–Shilov Spaces, and Continuity Properties of Localization Operators on Modulation Spaces

2018 ◽  
pp. 161-207
Author(s):  
Nenad Teofanov
Keyword(s):  
Modulation Spaces ◽  
Localization Operators ◽  
Continuity Properties

scholarly journals Bilinear Localization Operators on Modulation Spaces

2018 ◽  
Vol 2018 ◽  
pp. 1-10 ◽  
Author(s):  
Nenad Teofanov
Keyword(s):  
Pseudodifferential Operators ◽  
Linear Case ◽  
Modulation Spaces ◽  
Localization Operators ◽  
Continuity Properties

We introduce a class of bilinear localization operators and show how to interpret them as bilinear Weyl pseudodifferential operators. Such interpretation is well known in linear case whereas in bilinear case it has not been considered so far. Then we study continuity properties of both bilinear Weyl pseudodifferential operators and bilinear localization operators which are formulated in terms of a modified version of modulation spaces.

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.

scholarly journals Boundedness of localization operators on Lorentz mixed-normed modulation spaces

2014 ◽  
Vol 2014 (1) ◽  
pp. 430
Author(s):  
Ayşe Sandıkçı
Keyword(s):  
Modulation Spaces ◽  
Localization Operators
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