In this paper, we give a new covariation spectral representation of some non stationary symmetric α-stable processes (SαS). This representation is based on a weaker covariation pseudo additivity condition which is more general than the condition of independence. This work can be seen as a generalization of the covariation spectral representation of processes expressed as stochastic integrals wi...

Many natural objects, and in general layered materials, have non-linear reflection behaviour along the wavelengths. An accurate representation of phenomena such as interference and colour separation generally requires a fine spectral representation of light instead of the commonly used RGB components. In this article, we introduce and experiment with a general approach to create similar and con...

We give a representation of distributive lattices with the existential quantifier in terms of spectral spaces, which is an alternative to Cignoli’s representation in terms of Priestley spaces. Then we describe dual spectral spaces of subdirectly irreducible and simple Q-distributive lattices and prove that the variety QDist of Q-distributive lattices does not have the congruence extension prope...

This paper contains a survey of the spectral theory of periodically correlated and almost periodically correlated stochastic processes. These processes are also called cyclostationary and almost cyclostationary, and we give give some remarks concerning the historical development of the two nomenclatures. In this paper we survey the spectral theory of the covariance, the estimation of the Fourie...

We study heat semigroups generated by self-adjoint Laplace operators on metric graphs characterized by the property that the local scattering matrices associated with each vertex of the graph are independent from the spectral parameter. For such operators we prove a representation for the heat kernel as a sum over all walks with given initial and terminal edges. Using this representation a trac...

We study 3-point functions at finite temperature in the closed time path formalism. We give a general decomposition of the eight component tensor in terms of seven vertex functions. We derive a spectral representation for these seven functions in terms of two independent real spectral functions. We derive relationships between the seven functions and obtain a representation of the vertex tensor...

The spectral factorization problem of a scalar coercive spectral density is considered in the framework of the CallierDesoer algebra of distributed parameter system transfer functions. Criteria for the infinite product representation of a coercive spectral density and for the convergence of infinite product representations of spectral factors, i.e. for the convergence of the symmetric extractio...

Novel mathematical method called spectral measure method (SMM) is developed for characterization of bone structure and indirect estimation of bone properties. The spectral measure method is based on an inverse homogenization technique which allows to derive information about the structure of composite material from measured effective electric or viscoelastic properties. The mechanical propertie...

Reflected Brownian motion has been played an important role in economics, finance, queueing and many other fields. In this paper, we present the explicit spectral representation for the hitting time density of the reflected Brownian motion with two-sided barriers, and give some detailed analysis on the computational issues. Numerical analysis reveals that the spectral representation is more app...

We obtain a representation of the derivative of the spectral shift function ξ(λ, h) in the framework of semi-classical ”black box” perturbations. Our representation implies a meromorphic continuation of ξ(λ, h) involving the semi-classical resonances. Moreover, we obtain a Weyl type asymptotics of the spectral shift function as well as a Breit-Wigner approximation in an interval (λ− δ, λ+ δ), 0...