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Unions of graph Fourier multipliers are an important class of linear operators for processing signals defined on graphs. We present a novel method to efficiently distribute the application of these operators to the high-dimensional signals…
We use the method of similar operators to study a mixed problem for a differential equation with an involution and an operator-valued potential function. The differential operator defined by the equation is transformed into a similar…
Three types of integral representations for the cumulative distribution functions of convolutions of non-central p-variate gamma distributions are given by integration of elementary complex functions over the p-cube Cp =…
One of the key challenges in the area of signal processing on graphs is to design dictionaries and transform methods to identify and exploit structure in signals on weighted graphs. To do so, we need to account for the intrinsic geometric…
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the third paper, the analytical analysis of multiscale phenomena inherent in the…
The fractional integrals and fractional derivatives problem is tackled by using the operator approach. The definition domain E of operators is causal functions.Many properties of fractional integrals are given. Fractional derivatives…
This paper introduces a new global dynamics and chaos indicator based on the method of Lagrangian Descriptor apt for discriminating ordered and deterministic chaotic motions in multidimensional systems. The selected implementation of this…
Modern high-resolution microscopes, such as the scanning tunneling microscope, are commonly used to study specimens that have dense and aperiodic spatial structure. Extracting meaningful information from images obtained from such…
We study geometry of the phase space for finite-dimensional dynamical systems with degenerate Lagrangians. The Lagrangian and Hamiltonian constraint formalisms are treated as different local-coordinate pictures of the same invariant…
Motivated by a quaternionic formulation of quantum mechanics, we discuss quaternionic and complex linear differential equations. We touch only a few aspects of the mathematical theory, namely the resolution of the second order differential…
The Riemann-Liouville formula for fractional derivatives and integrals (differintegration) is used to derive formulae for matrix order derivatives and integrals. That is, the parameter for integration and differentiation is allowed to…
Factor graphs are a very powerful graphical representation, used to model many problems in robotics. They are widely spread in the areas of Simultaneous Localization and Mapping (SLAM), computer vision, and localization. In this paper we…
The symbolic manipulation program FORM is specialized to handle very large algebraic expressions. Some specific features of its internal structure make FORM very well suited for parallelization. We have now two parallel versions of FORM,…
This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…
As announced in [12], we develop a calculus of Fourier integral G-operators on any Lie groupoid G. For that purpose, we study convolability and invertibility of Lagrangian conic submanifolds of the symplectic groupoid T * G. We also…
When Fourier series are employed to solve partial differential equations, low-pass filters can be used to regularize divergent series that may appear. In this paper we show that the linear low-pass filters defined in a previous paper can be…
We develop statistical models for samples of distribution-valued stochastic processes featuring time-indexed univariate distributions, with emphasis on functional principal component analysis. The proposed model presents an intrinsic rather…
Interferometers play an increasingly important role for spatially resolved observations. If employed at full potential, interferometry can probe an enormous dynamic range in spatial scale. Interpretation of the observed visibilities…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
The aim of this paper is to investigate the boundedness of periodic Fourier integral operators in Lebesgue spaces with variable exponent $L^{p(\cdot)}$ on the $n$-dimensional torus. We deal with operators of type $(\rho, \delta)$ which…