Development of Linear Canonical Transforms: A Historical Sketch

DOI10.1007/978-1-4939-3028-9_1zbMath1334.78011OpenAlexW2295447232MaRDI QIDQ2799582

Kurt Bernardo Wolf

Publication date: 12 April 2016

Published in: Linear Canonical Transforms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4939-3028-9_1

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Applications of Lie groups to the sciences; explicit representations (22E70) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Applications of group representations to physics and other areas of science (20C35) Applications of linear algebraic groups to the sciences (20G45) Physical optics (78A10) Research exposition (monographs, survey articles) pertaining to optics and electromagnetic theory (78-02) Geometric optics (78A05)

Related Items (3)

Solving generalized wave and heat equations using linear canonical transform and sampling formulae ⋮ Hyperbolic linear canonical transforms of quaternion signals and uncertainty ⋮ Reduced phase space optics for general relativity: symplectic ray bundle transfer

Cites Work

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• A top-down account of linear canonical transforms
• A fast algorithm for the linear canonical transform
• Sampling and discretization of the linear canonical transform
• Sampling of linear canonical transformed signals
• Integral transforms in science and engineering
• Fractional transforms in optical information processing
• New 'coherent' states associated with non-compact groups
• Irreducible unitary representations of the Lorentz group
• Discrete fractional Fourier transform based on orthogonal projections
• Closed-form discrete fractional and affine Fourier transforms
• Discrete canonical transforms that are Hadamard matrices
• The Gel’fand realization and the exceptional representations of SL(2,R)
• On a Hilbert space of analytic functions and an associated integral transform part I
• Dependence ofs-waves on continuous dimension: The quantum oscillator and free systems
• Linear transformations and aberrations in continuous and finite systems
• The Clebsch–Gordan coefficients of the three-dimensional Lorentz algebra in the parabolic basis
• The Fractional Order Fourier Transform and its Application to Quantum Mechanics
• Canonical transforms. IV. Hyperbolic transforms: Continuous series of SL(2,R) representations
• Canonical transforms. I. Complex linear transforms
• Canonical transforms. II. Complex radial transforms
• Digital Computation of Linear Canonical Transforms
• The unitary irreducible representations of SL(2, R) in all subgroup reductions
• The discrete harmonic oscillator, Harper's equation, and the discrete fractional Fourier transform
• Symmetry Lie algebra of the Dirac oscillator
• Linear Canonical Transformations and Their Unitary Representations
• Canonical Transformations and Matrix Elements
• New forms for the representations of the three-dimensional Lorentz group
• Immersion of the Fourier Transform in a Continuous Group of Functional Transformations
• Lie methods in optics. II. Proceedings of the 2nd workshop held in Cocoyoc, Mexico, July 19--22, 1988

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