Related papers: Sampling theorems associated with offset linear ca…
This paper develops central limit theorems (CLT's) and large deviations results for additive functionals associated with reflecting diffusions in which the functional may include a term associated with the cumulative amount of boundary…
This tutorial is designed to clarify a few misconceptions in the field of ultrafast optics. (1) Analytic signal that underlies the complex-conjugate decomposition of the field is discussed, as well as the misunderstanding between…
This paper devotes to combine the chirp basis function transformation and symplectic coordinates transformation to yield a novel Wigner distribution (WD) associated with the linear canonical transform (LCT), named as the symplectic WD in…
Many empirical studies suggest that samples of continuous-time signals taken at locations randomly deviated from an equispaced grid (i.e., off-the-grid) can benefit signal acquisition, e.g., undersampling and anti-aliasing. However,…
The problem of estimating the spectrum of a density matrix is considered. Other problems, such as bipartite pure state entanglement, can be reduced to spectrum estimation. A local operations and classical communication (LOCC) measurement…
Many practical applications require the analysis of electromagnetic scattering properties of local structures using different sources of illumination. The Optical Theorem (OT) is a useful result in scattering theory, relating the extinction…
In most work to date, graph signal sampling and reconstruction algorithms are intrinsically tied to graph properties, assuming bandlimitedness and optimal sampling set choices. However, practical scenarios often defy these assumptions,…
Arguably the most widely used approaches for obtaining highly accurate molecular ground-state energies are coupled cluster methods. Despite introducing two layers of approximation, a linear and a nonlinear one, coupled cluster methods…
The orthogonality of cat and displaced cat states, underlying Heisenberg limited measurement in quantum metrology, is studied in the limit of large number of states. The asymptotic expression for the corresponding state overlap function,…
The paper is devoted to the development of the octonion Fourier transform (OFT) theory initiated in 2011 in articles by Hahn and Snopek. It is also a continuation and generalization of earlier work by Blaszczyk and Snopek, where they proved…
Under the high-dimensional setting that data dimension and sample size tend to infinity proportionally, we derive the central limit theorem (CLT) for linear spectral statistics (LSS) of large-dimensional sample covariance matrix. Different…
We derive an extension of the quantum regression theorem to calculate out-of-time-order correlation functions in Markovian open quantum systems. While so far mostly being applied in the analysis of many-body physics, we demonstrate that…
The linear canonical transform (LCT) was extended to complex-valued parameters, called complex LCT, to describe the complex amplitude propagation through lossy or lossless optical systems. Bargmann transform is a special case of the complex…
We develop a novel sampling theorem for functions defined on the three-dimensional rotation group SO(3) by connecting the rotation group to the three-torus through a periodic extension. Our sampling theorem requires $4L^3$ samples to…
In this paper, we extend the sampling theory on graphs by constructing a framework that exploits the structure in product graphs for efficient sampling and recovery of bandlimited graph signals that lie on them. Product graphs are graphs…
This research includes the study of some positive sampling Kantorovich operators (SK operators) and their convergence properties. A comprehensive analysis of both local and global approximation properties is presented using sampling…
Shannon's sampling theorem is one of the cornerstone topics that is well understood and explored, both mathematically and algorithmically. That said, practical realization of this theorem still suffers from a severe bottleneck due to the…
Conventional sampling and interpolation commonly rely on discrete measurements. In this paper, we develop a theoretical framework for extrapolation of signals in higher dimensions from knowledge of the continuous waveform on bounded…
We define a novel time-frequency analyzing tool, namely linear canonical wavelet transform (LCWT) and study some of its important properties like inner product relation, reconstruction formula and also characterize its range. We obtain…
The free metaplectic transformation (FMT) is widely used in many fields such as filter design, pattern recognition, image processing and optics. In order to obtain a more concise and intuitive convolution form, this paper studies two kinds…