A quaternionic analogue of the Segal-Bargmann transform

DOI10.1007/s11785-016-0609-5zbMath1364.44002arXiv1603.05052OpenAlexW2299761123MaRDI QIDQ523055

Kamal Diki, Allal Ghanmi

Publication date: 20 April 2017

Published in: Complex Analysis and Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1603.05052

zbMATH Keywords

slice regular functionsleft one-dimensional quaternionic Fourier transformquaternionic Segal-Bargmann transformslice hyperholomorphic Bargmann-Fock space

Mathematics Subject Classification ID

Special integral transforms (Legendre, Hilbert, etc.) (44A15) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Special families of functions of several complex variables (32A17) Holomorphic functions of several complex variables (32A10) Bergman spaces and Fock spaces (30H20)

Related Items (16)

Generalized Appell polynomials and Fueter–Bargmann transforms in the polyanalytic setting ⋮ The Segal–Bargmann Transform in Clifford Analysis ⋮ Slice Segal–Bargmann transform ⋮ Superoscillations and Fock spaces ⋮ Fock and Hardy spaces: Clifford Appell case ⋮ On the Mittag Leffler Bargmann (MLB) transform ⋮ Coherent state transforms and the Weyl equation in Clifford analysis ⋮ On the polyanalytic short-time Fourier transform in the quaternionic setting ⋮ Composition of Segal–Bargmann transforms ⋮ Clifford coherent state transforms on spheres ⋮ Polynomial approximation in slice regular Fock spaces ⋮ S-polyregular Bargmann spaces ⋮ On the Bargmann-Fock-Fueter and Bergman-Fueter integral transforms ⋮ On the quaternionic short-time Fourier and Segal-Bargmann transforms ⋮ The slice hyperholomorphic Bergman space on \(\mathbb {B}_{R}\): integral representation and asymptotic behavior ⋮ Segal-Bargmann transforms associated to a family of coupled supersymmetries

Cites Work

• Unnamed Item
• Noncommutative functional calculus. Theory and applications of slice hyperholomorphic functions
• The inverse Fueter mapping theorem
• Bounds on the Segal-Bargmann transform of \(L^p\) functions
• A new theory of regular functions of a quaternionic variable
• A new approach to Cullen-regular functions of a quaternionic variable
• Regular Functions of a Quaternionic Variable
• The Fock Space in the Slice Hyperholomorphic Setting
• Quaternion Reproducing Kernel Hilbert Spaces: Existence and Uniqueness Conditions
• The Fueter mapping theorem in integral form and the ℱ-functional calculus
• On a Hilbert space of analytic functions and an associated integral transform part I
• Towards a dictionary for the Bargmann transform
• Quaternion Fourier Transforms for Signal and Image Processing

This page was built for publication: A quaternionic analogue of the Segal-Bargmann transform