The hypergeometric Wigner and Weyl transforms attached to the Cherednik operators in the W-invariant case. Issue 9 (2nd September 2017)

• Record Type: Journal Article
• Authors: Chettaoui, Chirine; Hassini, Amina; Trimèche, Khalifa
• Is Part Of: Integral transforms and special functions. Volume 28:Issue 9(2017)
• Page Start: 663
• Page End: 681
• Publication Date: 2017-09-02
• Subjects: Root system BCd -- Cherednick operators -- hypergeometric Wigner transform -- hypergeometric Weyl transform -- hypergeometric Fourier transform; 33C67 -- 33E30 -- 43A32 -- 44A15; Integral transforms -- Periodicals; Transcendental functions -- Periodicals; Transformations (Mathematics) -- Periodicals; Calculus, Integral -- Periodicals; 515
• DOI: 10.1080/10652469.2017.1343315
• Languages: English
• ISSNs: 1065-2469

Abstract

ABSTRACT: Using the harmonic analysis associated to the Cherednik operators in the W-invariant case, relating to the root systemB C d, we define and study the Wigner and Weyl transformsW σ where σ is a symbol inS m, m ∈ R . We give the connection between these transforms, and criterias in terms of the symbol σ to prove the boundedness and compactness of the transformW σ .