On Schrödinger Oscillatory Integrals Associated with the Dunkl Transform
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DOI: 10.1007/s00041-018-9597-3
Abstract: In the paper we study the Schrödinger oscillatory integrals $$T^t_{\lambda ,a}f(x)$$Tλ,atf(x) ($$\lambda \ge 0$$λ≥0, $$a>1$$a>1) associated with the one-dimensional Dunkl transform $${\mathscr {F}}_{\lambda }$$Fλ. If $$a=2$$a=2, the function $$u(x,t):=T^t_{\lambda ,2}f(x)$$u(x,t):=Tλ,2tf(x) solves the free Schrödinger equation… read more here.
Keywords: schr dinger; oscillatory integrals; dunkl transform; dinger oscillatory ... See more keywords
A unified class of integral transforms related to the Dunkl transform
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DOI: 10.1016/j.jmaa.2016.12.054
Abstract: Abstract In the present paper, a new family of integral transforms depending on two parameters and related to the Dunkl transform is introduced. Well-known transforms, such as the fractional Dunkl transform, Dunkl transform, linear canonical… read more here.
Keywords: unified class; integral transforms; related dunkl; class integral ... See more keywords
A variety of uncertainty principles for the Dunkl transform on ℝd
Sign Up to like & getrecommendations! Published in 2020 at "Asian-european Journal of Mathematics"
DOI: 10.1142/s1793557121500777
Abstract: In this work, we prove Clarkson-type and Nash-type inequalities in the Dunkl setting on [Formula: see text] for [Formula: see text]-functions. By combining these inequalities, we show Heisenberg-type inequalities for the Dunkl transform on [Formula:… read more here.
Keywords: uncertainty; see text; formula see; type ... See more keywords
Logarithm Sobolev and Shannon's Inequalities Associated with the Deformed Fourier Transform and Applications
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DOI: 10.3390/sym14071311
Abstract: By using the symmetry of the Dunkl Laplacian operator, we prove a sharp Shannon-type inequality and a logarithmic Sobolev inequality for the Dunkl transform. Combining these inequalities, we obtain a new, short proof for Heisenberg-type… read more here.
Keywords: type; shannon; transform; logarithm sobolev ... See more keywords
Beurling’s Theorem for the Q-Fourier-Dunkl Transform
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DOI: 10.46793/kgjmat2101.039l
Abstract: 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… read more here.
Keywords: beurling theorem; dunkl transform; fourier dunkl; theorem fourier ... See more keywords