Related papers: Trigonometric splines in spectral problems
We describe the Dirichlet spectrum structure for the Fichera layers and crosses in any dimension $n\ge3$. Also the application of the obtained results to the classical Brownian exit times problem in these domains.
We explore the spectral properties of the time-dependent Maxwell's equations for a plane interface between a metamaterial represented by the Drude model and the vacuum, which fill respectively complementary half-spaces. We construct…
A short analysis is presented of the effects on the cepheid light curve shape, i.e. on the Fourier parameters usually adopted for its description, of the blending of the stellar image with other close stars. The conclusion is that, within…
The diffraction of ultrashort pulse changes its spatial and temporal structure that is crucial for multi-channel communication and location via such pulses. The features of the evolution of broadband pulses discussed for two general…
We analyze single particle coherence and interference in the presence of particle loss and derive an inequality that relates the preservation of coherence, the creation of superposition with the vacuum, and the degree of particle loss. We…
Three forms of representation of trigonometric interpolation splines are considered, in particular, the representation by the coefficients of the interpolation trigonometric polynomial, the representation by trigonometric B-splines, which…
Some spectral data analysis methods that are useful for the two-dimensional imaging diagnostics data are introduced. It is shown that the frequency spectrum, the local dispersion relation, the flow shear, and the nonlinear energy transfer…
The method of constructing trigonometric Hermite splines, which interpolate the values of some periodic function and its derivatives in the nodes of a uniform grid, is considered. The proposed method is based on the periodicity properties…
Optimization-based problems have become of great interest for signal approximation purposes, as they achieved good accuracy results while being extremely flexible and versatile. In this work, we put our focus on the context of periodic…
Time-frequency representations such as the spectrogram are commonly used to analyze signals having a time-varying distribution of spectral energy, but the spectrogram is constrained by an unfortunate tradeoff between resolution in time and…
We review several results related to the problem of a quantum particle in a random environment. In an introductory part, we recall how several functionals of the Brownian motion arise in the study of electronic transport in weakly…
Phase-space analysis or time-frequency analysis can be thought as Fourier analysis simultaneously both in time and in frequency, originating from signal processing and quantum mechanics. On groups having unitary Fourier transform, we…
A method is presented for investigating the periodic signal content of time series in which a number of signals is present, such as arising from the observation of multiperiodic oscillating stars in observational asteroseismology. Standard…
We derive exact equations that determine the spectra of undirected and directed sparsely connected regular graphs containing loops of arbitrary length. The implications of our results to the structural and dynamical properties of networks…
This survey addresses sampling discretization and its connections with other areas of mathematics. The survey concentrates on sampling discretization of norms of elements of finite-dimensional subspaces. We present here known results on…
One of the fundamental problems in communications is finding the energy distribution of signals in time and frequency domains. It should, therefore, be of great interest to find the most energy concentration hypercomplex signal. The present…
The temporal evolution of microwave pulses transmitted through random dielectric samples is obtained from the Fourier transform of field spectra. Large fluctuations are found in the local or single channel delay time, which is the first…
We analyze signal recovery when samples are taken concomitantly from a signal and its Fourier transform. This two-sided sampling framework extends classical one-sided reconstruction and is particularly useful when measurements in either…
It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation…
We investigate light propagation through materials with periodically modulated gain/loss profile in both transverse and longitudinal directions, i.e. in material with two-dimensional modulation in space. We predict effects of…