scholarly journals Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators

Author(s):  
Salem Ben Saïd ◽  
Asma Boussen ◽  
Mohamed Sifi

AbstractWe prove various versions of uncertainty principles for a certain Fourier transform ℱ

2021 ◽  
Vol 45 (01) ◽  
pp. 39-46
Author(s):  
EL MEHDI LOUALID ◽  
AZZEDINE ACHAK ◽  
RADOUAN DAHER

The Q-Fourier-Dunkl transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. By using the heat kernel associated to the Q-Fourier-Dunkl operator, we establish an analogue of Beurling’s theorem for the Q-Fourier-Dunkl transform ℱQ on ℝ.


2020 ◽  
Vol 35 (1) ◽  
pp. 043
Author(s):  
Azzedine Achak ◽  
Radouan Daher ◽  
Najat Safouane ◽  
El Mehdi Loualid

The Q-Fourier-Dunkl transform satisfies some uncertainty principles in a similar way to the Euclidean Fourier transform. By using theheat kernel associated to the Q-Fourier-Dunkl operator, we have established an analogue of Cowling-Price, Miyachi and Morgan theorems on $\mathbb{R}$ by using the heat kernel associated to the Q-Fourier-Dunkl transform.


2001 ◽  
Vol 711 ◽  
Author(s):  
Octavio Gomez-Martinez ◽  
Daniel H. Aguilar ◽  
Patricia Quintana ◽  
Juan J. Alvarado-Gil ◽  
Dalila Aldana ◽  
...  

ABSTRACTFourier Transform infrared spectroscopy has been employed to study the shells of two kind of mollusks, American oysters (Crassostrea virginica) and mussels (Ischadium recurvum). It is shown that it is possible to distinguish the different calcium carbonate lattice vibrations in each case, mussel shells present aragonite vibration frequencies, and the oyster shells present those corresponding to calcite. The superposition, shift and broadening of the infrared bands are discussed. Changes in the vibration modes due to successive thermal treatments are also reported.


2005 ◽  
Vol 11 (5) ◽  
pp. 535-546 ◽  
Author(s):  
Anna Kondakov ◽  
Buko Lindner

Bacterial glycolipids are complex amphiphilic molecules which are, on the one hand, of utmost importance for the organization and function of bacterial membranes and which, on the other hand, play a major role in the activation of cells of the innate and adaptive immune system of the host. Already small alterations to their chemical structure may influence the biological activity tremendously. Due to their intrinsic biological heterogeneity [number and type of fatty acids, saccharide structures and substitution with for example, phosphate ( P), 2-aminoethyl-(pyro)phosphate groups ( P-Etn) or 4-amino-4-deoxyarabinose (Ara4N)], separation of the different components are a prerequisite for unequivocal chemical and nuclear magnetic resonance structural analyses. In this contribution, the structural information which can be obtained from heterogenous samples of glycolipids by Fourier transform (FT) ion cyclotron resonance mass spectrometric methods is described. By means of recently analysed complex biological samples, the possibilities of high-resolution electrospray ionization FT-MS are demonstrated. Capillary skimmer dissociation, as well as tandem mass spectrometry (MS/MS) analysis utilizing collision-induced dissociation and infrared multiphoton dissociation, are compared and their advantages in providing structural information of diagnostic importance are discussed.


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