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...

We have investigated the spectral function of light quarks in infinite quark matter using a simple, albeit selfconsistent model [1]. Relations between the spectral function and the collisional self-energies in the Born approximation were used to calculate the spectral function in an iterative process beyond the quasiparticle approximation. The quark interactions were described by the SU(2) Namb...

Spectral methods constitute a useful tool in the analysis and synthesis of Boolean functions, especially in cases when other methods reduce to brute-force search procedures. There is renewed interest in the application of spectral methods in this area, which extends also to the closely connected concept of the autocorrelation function, for which spectral methods provide fast calculation algorit...

let ‎x be an ‎‎n-‎‎‎‎‎‎square complex matrix with the ‎cartesian decomposition ‎‎x = a + i ‎b‎‎‎‎‎, ‎where ‎‎a ‎and ‎‎b ‎are ‎‎‎n ‎‎times n‎ ‎hermitian ‎matrices. ‎it ‎is ‎known ‎that ‎‎$vert x vert_p^2 ‎leq 2(vert a vert_p^2 + vert b vert_p^2)‎‎‎$, ‎where ‎‎$‎p ‎‎geq 2‎$‎ ‎and ‎‎$‎‎vert . vert_p$ ‎is ‎the ‎schatten ‎‎‎‎p-norm.‎ ‎‎ ‎‎in this paper‎, this inequality and some of its improvements ...

This thesis presents an efficient approach to calculate dynamical properties of solids with strong electron correlations. The fast cluster method, a socalled finite temperature Lanczos method is combined with the Dynamical mean-field theory (DMFT) in order to study orbital degenerate systems as function of temperature. The full local Coulomb interaction was taken into account in all calculation...

The phonon spectral function of the one-dimensional Holstein model is obtained within weak and strong-coupling approximations based on analytical self-energy calculations. The characteristic excitations found in the limit of small charge-carrier density are related to the known (electronic) spectral properties of Holstein polarons such as the polaron band dispersion. Particular emphasis is laid...

We study the semi-classical behavior of the spectral function of the Schrödinger operator with short range potential. We prove that the spectral function is a semiclassical Fourier integral operator quantizing the forward and backward Hamiltonian flow relations of the system. Under a certain geometric condition we explicitly compute the phase in an oscillatory integral representation of the spe...

1.1 The main result. Given a map f : K → L of pointed CW complexes, let homf (K,L) denote the pointed space of pointed maps K → L, with f as the base point. Recall that a Πalgebra is a (≥ 1)-graded group with an action of the primary homotopy operations (for example, for any pointed topological space M there is a homotopy Π-algebra π∗M = {πiM}i=1). Given a map t : X → Y of Π-algebras, let homt(...

In this paper, the concept of generalized spectral function is introduced for finite-order tridiagonal symmetric matrices (Jacobi matrices) with complex entries. The structure of the generalized spectral function is described in terms of spectral data consisting of the eigenvalues and normalizing numbers of the matrix. The inverse problems from generalized spectral function as well as from spec...