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We study the morphology of convergence maps by perturbatively reconstructing their Minkowski Functionals (MFs). We present a systematics study using a set of three generalised skew-spectra as a function of source redshift and smoothing…
We study the phase-space concentration of the so-called generalized metaplectic operators whose main examples are Schr\"odinger equations with bounded perturbations. To reach this goal, we perform a so-called $\mathcal{A}$-Wigner analysis…
Conventional X-ray methods use incoming plane waves and result in discrete diffraction patterns when scattered at crystals. Here we find, by a systematic method, incoming waveforms which exhibit discrete diffraction patterns when scattered…
This paper is concerned with an inverse random source problem for the three-dimensional time-harmonic Maxwell equations. The source is assumed to be a centered complex-valued Gaussian vector field with correlated components, and its…
This paper proposes a standard way to represent sparse tensors. A broad theoretical framework for tensor data scattering methods used in various deep learning frameworks is established. This paper presents a theorem that is very important…
In [CPR2], we presented a K-theoretic approach to finding invariants of algebras with no non-trivial traces. This paper presents a new example that is more typical of the generic situation. This is the case of an algebra that admits only…
We develop an analytic approach to evaluating the density $\rho ({\cal E},\Gamma)$ of complex resonance poles with real energies $\mathcal{E}$ and widths $\Gamma$ in the pure reflection problem from a one-dimensional disordered sample with…
We construct the Atiyah-Hirzebruch spectral sequence (AHSS) for twisted differential generalized cohomology theories. This generalizes to the twisted setting the authors' corresponding earlier construction for differential cohomology…
Upcoming high spectral resolution telescopes, particularly Astro-H, are expected to finally deliver firm quantitative constraints on turbulence in the intra-cluster medium (ICM). We develop a new spectral analysis technique which exploits…
We study linear operators on a finite-dimensional space whose Kippenhahn curves consist of concentric circles centered at the origin. We say that such operators have Circularity property. One class of examples is rotationally invariant…
Using general principles in the theory of vertex operator algebras and their twisted modules, we obtain a bosonic, twisted construction of a certain central extension of a Lie algebra of differential operators on the circle, for an…
The operator realizing a Dehn twist in quantum Teichmuller theory is diagonalized and continuous spectrum is obtained. This result is in agreement with the expected spectrum of conformal weights in quantum Liouville theory at c>1. The…
We study the resonance fluorescence properties of an optically active spin 1/2 system, elucidating the effects of a magnetic field on the coherence of the scattered light. We derive a master equation model for this system that reproduces…
We provide an abstract framework for singular one-dimensional Schroedinger operators with purely discrete spectra to show when the spectrum plus norming constants determine such an operator completely. As an example we apply our findings to…
Tensors are multiway arrays of data, and transverse operators are the operators that change the frame of reference. We develop the spectral theory of transverse tensor operators and apply it to problems closely related to classifying…
Coherent continuous wave (CW) terahertz spectroscopy is an extremely valuable technique that allows for the interrogation of systems that exhibit narrow resonances in the terahertz (THz) frequency range, such as high-quality (high-Q) THz…
The Z Transform is a mathematical operation in signal processing, which gives a tractable way to solve linear, constant-coefficient difference equations. Based on the classical Z transform and inspired by the thought of sliding DFT, a new…
In a thin multidimensional layer we consider a second order differential PT-symmetric operator. The operator is of rather general form and its coefficients are arbitrary functions depending both on slow and fast variables. The PT-symmetry…
We summarize our recent determination [1] of the spectral density of the Wilson operator in the p-regime of Wilson chiral perturbation theory. We discuss the range of validity of our formula and a possible extension to our computation in…
While General Fractional Calculus has successfully expanded the scope of memory operators beyond power-laws, standard formulations remain predominantly restricted to the half-line via Riemann-Liouville or Caputo definitions. This constraint…