Jacobi ϑ-functions and discrete Fourier transforms

DOI10.1063/1.2209770zbMath1112.33014arXivmath-ph/0604018OpenAlexW2012101105MaRDI QIDQ3441936

M. Ruzzi

Publication date: 16 May 2007

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math-ph/0604018

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) General mathematical topics and methods in quantum theory (81Q99) Fourier coefficients, Fourier series of functions with special properties, special Fourier series (42A16) Elliptic functions and integrals (33E05)

Related Items (12)

Paths of zeros of analytic functions describing finite quantum systems ⋮ Discrete Fourier transform of prime order: eigenvectors with small support ⋮ Discrete Fourier Transform and Theta Function Identities ⋮ Orbital angular momentum in phase space ⋮ Theoretical formulation of finite-dimensional discrete phase spaces. I: Algebraic structures and uncertainty principles ⋮ Theoretical formulation of finite-dimensional discrete phase spaces. II. On the uncertainty principle for Schwinger unitary operators ⋮ Discrete phase-space mappings, tomographic condition and permutation invariance ⋮ Discrete Fourier Transform and Extended Modified Hermite Polynomials ⋮ DISCRETE COHERENT STATES FOR n QUBITS ⋮ Analytic representations with theta functions for systems on ℤ(d) and on 𝕊 ⋮ Discrete Fourier transform and Jacobi θ function identities ⋮ Unnamed Item

Cites Work

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• The construction of orthonormal bases diagonalizing the discrete Fourier transform
• Discrete coherent states and probability distributions in finite-dimensional spaces
• UNITARY OPERATOR BASES
• Eigenvalues and eigenvectors of the finite Fourier transform
• String Theory
• Coherent states for a quantum particle on a circle
• Analytic representation of finite quantum systems
• Wigner distribution function for finite systems

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