TY - JOUR
T1 - Uncertainty principles and characterization of the heat kernel for certain differential-reflection operators
AU - Ben Saïd, Salem
AU - Boussen, Asma
AU - Sifi, Mohamed
N1 - Publisher Copyright:
© 2015 by De Gruyter.
PY - 2015/10/1
Y1 - 2015/10/1
N2 - We prove various versions of uncertainty principles for a certain Fourier transform FA. Here, A is a Chébli function (that is, a Sturm-Liouville function with additional hypotheses). We mainly establish an analogue of Beurling's theorem, and its relatives such as theorems of Gelfand-Shilov type, of Morgan type, of Hardy type, and of Cowling-Price type, for FA and relate them to the characterization of the heat kernel corresponding to FA. Heisenberg's and local uncertainty inequalities are also proved.
AB - We prove various versions of uncertainty principles for a certain Fourier transform FA. Here, A is a Chébli function (that is, a Sturm-Liouville function with additional hypotheses). We mainly establish an analogue of Beurling's theorem, and its relatives such as theorems of Gelfand-Shilov type, of Morgan type, of Hardy type, and of Cowling-Price type, for FA and relate them to the characterization of the heat kernel corresponding to FA. Heisenberg's and local uncertainty inequalities are also proved.
KW - Differential-reflection operators
KW - heat kernel
KW - uncertainty principles
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U2 - 10.1515/apam-2015-5010
DO - 10.1515/apam-2015-5010
M3 - Article
AN - SCOPUS:84943805825
SN - 1867-1152
VL - 6
SP - 215
EP - 239
JO - Advances in Pure and Applied Mathematics
JF - Advances in Pure and Applied Mathematics
IS - 4
ER -