Fouriertransformation auf dünnen Gittern mit hierarchischen Basen.
Gegenbauer polynomials and semiseparable matrices.
Linear transforms supporting circular convolution over a commutative ring with identity
We consider a commutative ring with identity and a positive integer . We characterize all the 3-tuples of linear transforms over , having the “circular convolution” property, i.eṡuch that for all .
Logarithm of the discrete Fourier transform.
Numerical analysis of the MFS for certain harmonic problems
The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices that arise when the MFS is applied to the Dirichlet problem for Laplace’s equation in a disk. In particular, we study the behaviour of the eigenvalues of these matrices and the cases in which they vanish. Based on this, we propose a modified efficient numerical algorithm for the solution of the problem...
Numerical analysis of the MFS for certain harmonic problems
The Method of Fundamental Solutions (MFS) is a boundary-type meshless method for the solution of certain elliptic boundary value problems. In this work, we investigate the properties of the matrices that arise when the MFS is applied to the Dirichlet problem for Laplace's equation in a disk. In particular, we study the behaviour of the eigenvalues of these matrices and the cases in which they vanish. Based on this, we propose a modified efficient numerical algorithm for the solution of the problem...
O matematice v mobilu
On discrete Fourier analysis of amplitude and phase modulated signals
In this work the problem of characterization of the Discrete Fourier Transform (DFT) spectrum of an original complex-valued signal , t=0,1,...,n-1, modulated by random fluctuations of its amplitude and/or phase is investigated. It is assumed that the amplitude and/or phase of the signal at discrete times of observation are distorted by realizations of uncorrelated random variables or randomly permuted sequences of complex numbers. We derive the expected values and bounds on the variances of such...
On integer sequences associated with the cyclic and complete graphs.
On orthonormal product systems.
On the computation of the GCD of 2-D polynomials
The main contribution of this work is to provide an algorithm for the computation of the GCD of 2-D polynomials, based on DFT techniques. The whole theory is implemented via illustrative examples.
On the discrete harmonic wavelet transform.
Periodické distribuce a diskrétní Fourierova transformace
Převod přenosů ze spojité Laplaceovy transformace do transformace
Signal reconstruction from given phase of the Fourier transform using Fejér monotone methods
The aim is to reconstruct a signal function x ∈ L₂ if the phase of the Fourier transform [x̂] and some additional a-priori information of convex type are known. The problem can be described as a convex feasibility problem. We solve this problem by different Fejér monotone iterative methods comparing the results and discussing the choice of relaxation parameters. Since the a-priori information is partly related to the spectral space the Fourier transform and its inverse have to be applied in each...
Solving singular convolution equations using the inverse fast Fourier transform
The inverse Fast Fourier Transform is a common procedure to solve a convolution equation provided the transfer function has no zeros on the unit circle. In our paper we generalize this method to the case of a singular convolution equation and prove that if the transfer function is a trigonometric polynomial with simple zeros on the unit circle, then this method can be extended.
Stability results for scattered data interpolation on the rotation group.
The Fourier Analysis of Bezier Curves
Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping
In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for the...
Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping
In this paper, we study a Zakharov system coupled to an electron diffusion equation in order to describe laser-plasma interactions. Starting from the Vlasov-Maxwell system, we derive a nonlinear Schrödinger like system which takes into account the energy exchanged between the plasma waves and the electrons via Landau damping. Two existence theorems are established in a subsonic regime. Using a time-splitting, spectral discretizations for the Zakharov system and a finite difference scheme for...