Related papers: Trigonometric splines in spectral problems
It has been observed that an interesting class of non-Gaussian stationary processes is obtained when in the harmonics of a signal with random amplitudes and phases, frequencies can also vary randomly. In the resulting models, the…
We study the set of localizations of an integral domain from a topological point of view, showing that it is always a spectral space and characterizing when it is a proconstructible subspace of the space of all overrings. We then study the…
Diffraction in time of a particle confined in a box which its walls are removed suddenly at $t=0$ is studied. The solution of the time-dependent Schr\"{o}dinger equation is discussed analytically and numerically for various initial…
For a long time, many methods are developed to make temporal signal analyses based on time series. However, for geographical systems, spatial signal analyses are as important as temporal signal analyses. Nonstationary spatial and temporal…
A system of strongly interacting fermions in a solid state is discussed. A structure of singlet and triplet coupled 2-particle states and their excitation spectra are investigated. It is shown that an account of intersite fermion…
The paper studies properties of continuous time processes with spectrum degeneracy at a single point where their Fourier transforms vanish with a certain rate. It appears that these processes are linearly predictable in some weak sense,…
Photonic crystal fibers are used in fiber amplifiers and lasers because of the flexibility in the design of mode area and dispersion. However, these quantities depend strongly on the wavelength. The wavelength dependence of gain,…
Calculations of frequency spectra for organic molecular crystals taking various defects in their structure into account are carried out. It is shown how the presence of the vacancies, orientation disorder, and surface presence affects…
The "theoretical limit of time-frequency resolution in Fourier analysis" is thought to originate in certain mathematical and/or physical limitations. This, however, is not true. The actual origin arises from the numerical (technical) method…
In recent years the topic of localized wave solutions of the homogeneous scalar wave equation, i.e., the wave fields that propagate without any appreciable spread or drop in intensity, has been discussed in many aspects in numerous…
We follow a stream of the history of positive matrices and positive functionals, as applied to algebraic sums of squares decompositions, with emphasis on the interaction between classical moment problems, function theory of one or several…
We study the dispersive properties of a linear equation in one spatial dimension which is inspired by models in peridynamics. The interplay between nonlocality and dispersion is analyzed in detail through the study of the asymptotics at low…
The spectral analysis of the operator Fourier truncated on the positive half-axis is done.
We present an amelioration of current known algorithms for optimal spectral partitioning problems. The idea is to use the advantage of a representation using density functions while decreasing the computational time. This is done by…
A major issue in harmonic analysis is to capture the phase dependence of frequency representations, which carries important signal properties. It seems that convolutional neural networks have found a way. Over time-series and images,…
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…
This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to…
Remotely measuring subsurface water currents from imagery of the wave field has become a much-used technique. We study the biases and errors in such measurements due to spectral leakage, and suggest mitigating procedures. Deviations between…
We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the fields of signal processing, harmonic analysis and sparse…
This is the first in a series of two papers investigating the effect of electron-phonon coupling in two-dimensional Fourier transformed electronic spectroscopy. We present a series of one- and two-dimensional nonlinear spectroscopic…