Is computing with the finite Fourier transform pure or applied mathematics?
From MaRDI portal
Publication:3931844
DOI10.1090/S0273-0979-1979-14686-XzbMath0475.42014OpenAlexW2069384709MaRDI QIDQ3931844
Louis Auslander, Richard Tolimieri
Publication date: 1979
Published in: Bulletin of the American Mathematical Society (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1090/s0273-0979-1979-14686-x
History of mathematics in the 20th century (01A60) Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type (42A38) Numerical methods for trigonometric approximation and interpolation (65T40) History of numerical analysis (65-03)
Related Items
Gruppentheoretische aspekte der signalübertragung und der kardinalen interpolationssplines I ⋮ Discrete Fourier transform tensors and their eigenvalues ⋮ The Frobenius formalism in Galois quantum systems ⋮ Finite fields and Ramanujan graphs ⋮ Discrete Fourier Transform Tensors and Their Ranks ⋮ Discrete Fourier transform of prime order: eigenvectors with small support ⋮ On a Discrete Number Operator Associated with the 5D Discrete Fourier Transform ⋮ Attenuation factors and nilpotent harmonic analysis ⋮ Zeros of Dirichlet series ⋮ Discrete Fourier Transform and Theta Function Identities ⋮ Separation of variables and the computation of Fourier transforms on finite groups. II ⋮ Groups and Symmetries in Numerical Linear Algebra ⋮ Maximally symmetric stabilizer MUBs in even prime-power dimensions ⋮ Maximal scarring for eigenfunctions of quantum graphs ⋮ Discrete Fourier transform and Riemann identities for \(\theta\) functions ⋮ Fast Fourier analysis for abelian group extensions ⋮ On the Discrete Fourier Transform Eigenvectors and Spontaneous Symmetry Breaking ⋮ Hecke's theorem in quadratic reciprocity, finite nilpotent groups and the Cooley-Tukey algorithm ⋮ Harmonic analysis on finite Heisenberg groups. ⋮ Some mathematical considerations on solid state physics in the framework of the phase space formulation of quantum mechanics ⋮ \(L\)-functions for Jacobi forms of arbitrary degree ⋮ The Algebra of the Finite Fourier Transform and Coding Theory ⋮ Index and dynamics of quantized contact transformations ⋮ QUANTUM DESIGNS: FOUNDATIONS OF A NONCOMMUTATIVE DESIGN THEORY ⋮ On supersymmetric eigenvectors of the 5D discrete Fourier transform ⋮ Continuity properties of the Gabor frame operator ⋮ An algebraic interpretation of the intertwining operators associated with the discrete Fourier transform ⋮ An exercise(?) in Fourier analysis on the Heisenberg group ⋮ Zeros of the Davenport-Heilbronn counterexample ⋮ Quantum systems with finite Hilbert space and Chebyshev polynomials ⋮ Maximally equiangular frames and Gauss sums ⋮ Discrete Fourier Transform and Extended Modified Hermite Polynomials ⋮ Spectral properties of small Hadamard matrices ⋮ Unnamed Item ⋮ Efficient Computation of the Fourier Transform on Finite Groups ⋮ Dimension of the commutant for the SU(N) affine algebras ⋮ On the diagonalization of the discrete Fourier transform ⋮ The determination of Gauss sums ⋮ Double coset decompositions and computational harmonic analysis on groups ⋮ Unnamed Item ⋮ ON q-EXTENSIONS OF MEHTA'S EIGENVECTORS OF THE FINITE FOURIER TRANSFORM ⋮ Winograd's Fourier transform via circulants ⋮ The eigenvectors of the discrete Fourier transform: A version of the Hermite functions ⋮ The construction of orthonormal bases diagonalizing the discrete Fourier transform ⋮ Finite Fourier transform for functions with restricted support ⋮ Right division in groups, Dedekind-Frobenius group matrices, and Ward quasigroups. ⋮ Abelian semi-simple algebras and algorithms for the discrete Fourier transform ⋮ Stabilité et convergence des méthodes spectrales polynômiales. Application à l'équation d'advection
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Abelian harmonic analysis, theta functions and function algebras on a nilmanifold
- Harmonic analysis on compact solvmanifolds
- On the multiplicative complexity of the discrete Fourier transform
- Sur certains groupes d'opérateurs unitaires
- Translation-invariant subspaces in L\(^2\) of a compact nilmanifold. I
- Analogues of Poisson's Summation Formula
- On computing the Discrete Fourier Transform
- Some bilinear forms whose multiplicative complexity depends on the field of constants
- The multiplicity problem for 4-dimensional solvmanifolds
- [https://portal.mardi4nfdi.de/wiki/Publication:4173773 Algebraic Structures for � Σ n 1 L 2 (Z/n) Compatible with the Finite Fourier Transform]
- An Algorithm for the Machine Calculation of Complex Fourier Series
- On the number of multiplications necessary to compute certain functions
- Harmonic Analysis on Nilmanifolds