Related papers: A factorization of a L\'evy process over a phase-t…
I discuss a formula decomposing the integral of time-ordered products of operators into sums of products of integrals of time-ordered commutators. The resulting factorization enables summation of an infinite series to be carried out to…
A generalized definition of superpotential has proposed, which connects two one-dimensional potentials $V_{1}$ and $V_{2}$ with discrete energy spectra completely and where: 1) energy of factorization equals to arbitrary level of spectrum…
A matrix factorization problem is considered. The matrix to be factorized is algebraic, has dimension 2 X 2 and belongs to Moiseev's class. A new method of factorization is proposed. First, the matrix factorization problem is reduced to a…
Following from recent developments by Hubalek and Kyprianou, the objective of this paper is to provide further methods for constructing new families of scale functions for spectrally negative L\'evy processes which are completely explicit.…
The scattering matrix for the full-line matrix Schr\"odinger equation is analyzed when the corresponding matrix-valued potential is selfadjoint, integrable, and has a finite first moment. The matrix-valued potential is decomposed into a…
We present and demonstrate a version of Levinson's theorem especially dedicated to the asymptotic behavior of form factor phases. Indeed, as required by analyticity, form factors are multi-valued complex functions of a square four-momentum…
We study processes with unstable particles in intermediate time-like states. It is shown that the amplitudes squared of such processes factor exactly in the framework of the model of unstable particles with continuous masses. Decay widths…
We discuss the Gamma Levy process, including path properties, the inverse process, integrability, and its spin-offs obtained by compounding, exponentiation, and other operations; further extendable to arbitrary sigma-finite continuous Borel…
We suggest new closely related methods for numerical inversion of $Z$-transform and Wiener-Hopf factorization of functions on the unit circle, based on sinh-deformations of the contours of integration, corresponding changes of variables and…
Long-time limit of one-dimensional L\'{e}vy processes weighted and normalized with respect to the exponential functional of two-point local times are studied. The limit processes may vary according to the choice of random clocks.
We provide a novel expression of the scale function for a L\'evy processes with negative phase-type jumps. It is in terms of a certain transition rate matrix which is explicit up to a single positive number. A monotone iterative scheme for…
Path decomposition is performed to characterize the law of the pre/post-supremum, post-infimum and the intermediate processes of a spectrally negative Levy process taken up to an independent exponential time T: As a result, mainly the…
We generalize the Wiener-Hopf factorization of Laurent series to more general commutative coefficient rings, and we give explicit formulas for the decomposition. We emphasize the algebraic nature of this factorization.
In the path integral formulation of quantum mechanics, the phase factor Exp[iS(x[t])] is associated with every path x[t]. Summing this factor over all paths yields Feynman's propagator as a sum-over-paths. In the original formulation, the…
The last couple of years has seen a remarkable number of new, explicit examples of the Wiener-Hopf factorization for Levy processes where previously there had been very few. We mention in particular the many cases of spectrally negative…
We study factorization of processes involving two fragmentation functions in the case of very small transverse momenta. We consider two-hadron production in inclusive $e^+ e^-$ annihilation and demonstrate a new simple and illustrative…
In this paper, we study the cut-off phenomenon under the total variation distance of $d$-dimensional Ornstein-Uhlenbeck processes which are driven by L\'evy processes. That is to say, under the total variation distance, there is an abrupt…
In this paper, we investigate the uniqueness of the phase retrieval problem for the fractional Fourier transform (FrFT) of variable order. This problem occurs naturally in optics and quantum physics. More precisely, we show that if $u$ and…
We develop a method that relates the truncated cumulant-function of the fourth order with the L\'evian cumulant-function. This gives us explicit formulas for the L\'evy-parameters, which allow a real-time analysis of the state of a…
We analyze transverse thrust in the framework of Soft Collinear Effective Theory and obtain a factorized expression for the cross section that permits resummation of terms enhanced in the dijet limit to arbitrary accuracy. The factorization…