Modulation spacesMp,qfor0<p,q≦∞

The purpose of this paper is to construct modulation spacesMp,q(Rd)for general0<p,q≦∞, which coincide with the usual modulation spaces when1≦p,q≦∞, and study their basic properties including their completeness. Given anyg∈S(Rd)such that suppĝ⊂ {ξ∣|ξ|≦1}and∑k∈Zdĝ(ξ-αk)≡1, our modulation space consists of all tempered distributionsfsuch that the (quasi)-norm‖f‖M[g]p,q:≔(∫Rd(∫Rd|f*(Mωg)(x)|pdx)qpdω)1qis finite.

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Position operator

Journal of Mathematical Economics and Finance ◽

10.14505//jmef.v4.1(6).05 ◽

2018 ◽

Vol 4 (1(6)) ◽

pp. 79

Author(s):

David Carfì

Keyword(s):

Position Operator ◽

Tempered Distributions ◽

Basic Properties

In this paper, we introduce the position operator on the space of the tempered distributions, with some its fundamental basic properties.

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Positivity in twisted convolution algebra and Fourier modulation spaces

Bulletin Classe des sciences mathematiques et natturalles ◽

10.2298/bmat0631010t ◽

2006 ◽

Vol 133 (31) ◽

pp. 75-86

Author(s):

J. Toft

Keyword(s):

Subject Classification ◽

Modulation Space ◽

Modulation Spaces ◽

Twisted Convolution ◽

Convolution Algebra

Let Wp,q be the Fourier modulation space FMp,q and let *? be the twisted convolution. I? ? ? D' such that (a *? ?,?)? 0 for every ? ? C?0, and ? ? such that X(0) ? 0, then we prove that ?? ? Wp,? iff ? ? Wp,?. We also present some extensions to the case when weighted Fourier modulation spaces are used. AMS Mathematics Subject Classification (2000): 47B65, 35A21, 35S05.

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Subexponential decay and regularity estimates for eigenfunctions of localization operators

Journal of Pseudo-Differential Operators and Applications ◽

10.1007/s11868-021-00383-1 ◽

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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Smooth pointwise multipliers of modulation spaces

Analele Universitatii Ovidius Constanta - Seria Matematica ◽

10.2478/v10309-012-0021-8 ◽

2012 ◽

Vol 20 (1) ◽

pp. 317-328 ◽

Cited By ~ 1

Author(s):

Ghassem Narimani

Keyword(s):

Multiplication Operator ◽

Modulation Space ◽

Modulation Spaces ◽

Potential Space ◽

Bessel Potential ◽

Pointwise Multiplication ◽

Bessel Potential Space ◽

Pointwise Multipliers ◽

Conjugate Exponent

Abstract Let 1 < p, q < ∞ and s, r ∈ ℝ. It is proved that any function in the amalgam space W(Hrp(ℝd), ℓ∞), where p' is the conjugate exponent to p and Hrp′ (ℝd) is the Bessel potential space, defines a bounded pointwise multiplication operator in the modulation space Msp,q(ℝd), whenever r > |s| + d

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On the Essence and Tipology of International Public Goods

Voprosy Ekonomiki ◽

10.32609/0042-8736-2005-3-131-141 ◽

2005 ◽

pp. 131-141

Author(s):

V. Mortikov

Keyword(s):

Economic Policy ◽

Social Construction ◽

Public Goods ◽

Public Good ◽

Global Public Goods ◽

Club Goods ◽

Basic Properties ◽

International Public Goods ◽

Regional Public Goods ◽

Joint Products

The basic properties of international public goods are analyzed in the paper. Special attention is paid to the typology of international public goods: pure and impure, excludable and nonexcludable, club goods, regional public goods, joint products. The author argues that social construction of international public good depends on many factors, for example, government economic policy. Aggregation technologies in the supply of global public goods are examined.

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