scholarly journals Positivity in twisted convolution algebra and Fourier modulation spaces

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.

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 Smooth pointwise multipliers of modulation spaces

2012 ◽  
Vol 20 (1) ◽  
pp. 317-328 ◽  
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

KMS states for reduced groups, theta functions and the Powers–Størmer construction

1989 ◽  
Vol 105 (2) ◽  
pp. 397-410 ◽  
Author(s):  
K. C. Hannabuss
Keyword(s):  
Fock Space ◽  
Theta Functions ◽  
Loop Groups ◽  
Vector Group ◽  
Kms States ◽  
Twisted Convolution ◽  
Fock States ◽  
Convolution Algebra ◽  
Schwartz Functions ◽  
Space Construction

AbstractKMS states of a twisted convolution algebra of Schwartz functions on a vector group are classified and related to KMS states of twisted L1-algebras for certain subquotients. The KMS states for the subquotient algebras are also related to Fock states of vector groups. In the particular case of the subquotient Tn × ℤn of ℚ2n this links the Fock space construction of the theta functions with their appearance in KMS states of loop groups and in the Kac character formula.

scholarly journals Modulation spacesMp,qfor0

2006 ◽  
Vol 4 (3) ◽  
pp. 329-341 ◽  
Author(s):  
Masaharu Kobayashi
Keyword(s):  
Modulation Space ◽  
Modulation Spaces ◽  
Tempered Distributions ◽  
Basic Properties

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.

Classical Tauberian Theorems for the (C; 1; 1) Summability Method

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Ümit Totur
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Subject Classification ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Littlewood Theorem

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0

Some Properties of Para-Sasakian Manifolds

2017 ◽  
Vol 5 (2) ◽  
pp. 73-78
Author(s):  
Jay Prakash Singh ◽  
Keyword(s):  
Vector Field ◽  
Killing Vector ◽  
Sasakian Manifold ◽  
Subject Classification ◽  
Killing Vector Field ◽  
Sasakian Manifolds ◽  
Geometric Properties ◽  
Paper Author

In this paper author present an investigation of some differential geometric properties of Para-Sasakian manifolds. Condition for a vector field to be Killing vector field in Para-Sasakian manifold is obtained. Mathematics Subject Classification (2010). 53B20, 53C15.

scholarly journals Multiclass emotion prediction using heart rate and virtual reality stimuli

2021 ◽  
Vol 8 (1) ◽  
Author(s):  
Aaron Frederick Bulagang ◽  
James Mountstephens ◽  
Jason Teo
Keyword(s):  
Heart Rate ◽  
Virtual Reality ◽  
Nearest Neighbor ◽  
Subject Classification ◽  
Support Vector ◽  
Display Device ◽  
K Nearest Neighbor ◽  
Potential Applications ◽  
Health Rehabilitation ◽  
Emotion Model

Abstract Background Emotion prediction is a method that recognizes the human emotion derived from the subject’s psychological data. The problem in question is the limited use of heart rate (HR) as the prediction feature through the use of common classifiers such as Support Vector Machine (SVM), K-Nearest Neighbor (KNN) and Random Forest (RF) in emotion prediction. This paper aims to investigate whether HR signals can be utilized to classify four-class emotions using the emotion model from Russell’s in a virtual reality (VR) environment using machine learning. Method An experiment was conducted using the Empatica E4 wristband to acquire the participant’s HR, a VR headset as the display device for participants to view the 360° emotional videos, and the Empatica E4 real-time application was used during the experiment to extract and process the participant's recorded heart rate. Findings For intra-subject classification, all three classifiers SVM, KNN, and RF achieved 100% as the highest accuracy while inter-subject classification achieved 46.7% for SVM, 42.9% for KNN and 43.3% for RF. Conclusion The results demonstrate the potential of SVM, KNN and RF classifiers to classify HR as a feature to be used in emotion prediction in four distinct emotion classes in a virtual reality environment. The potential applications include interactive gaming, affective entertainment, and VR health rehabilitation.

scholarly journals Metabolic connectivity-based single subject classification by multi-regional linear approximation in the rat

NeuroImage ◽  
2021 ◽  
Vol 235 ◽  
pp. 118007
Author(s):  
Maximilian Grosch ◽  
Leonie Beyer ◽  
Magdalena Lindner ◽  
Lena Kaiser ◽  
Seyed-Ahmad Ahmadi ◽  
...  
Keyword(s):  
Linear Approximation ◽  
Subject Classification ◽  
Single Subject ◽  
Metabolic Connectivity
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