We consider a class of random lattice operators including Sc hr odinger operators of the form H = + w + gv; where w(x) is a real-valued periodic function, g is a positive constant and v(x); x 2 Zd; are independent, identically distributed real random variables. We prov e that if the operator + w has gaps in the spectrum and g is su ciently small, then the operator H develops pure point spectru...

In this paper we introduce Baxter integral Q-operators for finite-dimensional Lie algebras gll+1 and so2l+1. Whittaker functions corresponding to these algebras are eigenfunctions of the Q-operators with the eigenvalues expressed in terms of Gammafunctions. The appearance of the Gamma-functions is one of the manifestations of an interesting connection between Mellin-Barnes and Givental integral...

where N is a nonlinear operator over a real Hilbert space S and E is a linear differential operator over a bounded domain G of R" with homogeneous boundary conditions and possessing a finite-dimensional kernel. The particular case when NU = g(u) +f has been the subject of much study in recent years and sufficient conditions in terms of g(co), g(-co) and f, patterned after the results of [8], ha...

Some necessary and sufficient conditions are given for the existence of a G-positive (G-repositive) solution to adjointable operator equations $AX=C,AXA^{left( astright) }=C$ and $AXB=C$ over Hilbert $C^{ast}$-modules, respectively. Moreover, the expressions of these general G-positive (G-repositive) solutions are also derived. Some of the findings of this paper extend some known results in the...

Abstract. In this paper, we mainly parameterize g-frames in Hilbert space in terms of operators. Firstly, under the condition that there exists a g-orthonormal basis we establish the one to one correspondence between different kinds of g-frames with certain kinds of operators. Then we parameterize g-frames without the above restriction. Finally, we consider some special g-frames, and their oper...

One of the difficulties in seeing beneath salt is that the migration velocity in the salt and above is not well known. This can lead to defocusing of migration images beneath the salt. In this paper we show that reduced-time migration (RTM) and interferometric migration (IM) can mitigate this problem. Reduced-time migration shifts the data with the time difference between the calculated arrival...

We show that the general Levy process can be embedded in a suitable Fock space, classified by cocycles of the real line regarded as a group. The formula of de Finetti corresponds to coboundaries. Kolmogorov’s processes correspond to cocycles of which the derivative is a cocycle of the Lie algebra of R. The Lévy formula gives the general cocycle. 1 Cyclic representations of groups Let G be a gro...

In this work we show a result of existence positive solution for the following nonlocal problem Kirchhoff type \(-M\biggl(\int_{\Omega} |\nabla u|^{2} dx\biggl)\Delta u= f(u)-a\) in \(\Omega\), \(u=0\) on \(\partial\Omega,\) where \(\Omega \subset\mathbf{R}^{N}\) is smooth bounded domain, \(M,f\) are continuous nonnegative functions and \(a>0\). By using mainly variational methods, prove \(a\) ...