in this work‎, ‎an iterative method based on a matrix form of lsqr algorithm is constructed for solving the linear operator equation $mathcal{a}(x)=b$‎ ‎and the minimum frobenius norm residual problem $||mathcal{a}(x)-b||_f$‎ ‎where $xin mathcal{s}:={xin textsf{r}^{ntimes n}~|~x=mathcal{g}(x)}$‎, ‎$mathcal{f}$ is the linear operator from $textsf{r}^{ntimes n}$ onto $textsf{r}^{rtimes s}$‎, ‎$ma...

For the approximation of fixed points of a nonexpansive operator T in a uniformly convex Banach space E the convergence of the Mann-Toeplitz iteration x„+1 = a„T(x„) + (1 a„)xñ is studied. Strong convergence is established for a special class of operators T. Via regularization this result can be used for general nonexpansive operators, if E possesses a weakly sequentially continuous duality map...

Kirchhoo migration operator is a highly oscillatory integral operator. In our previous work (see \Seismic Imaging in Wavelet Domain", Wu and Yang 1], 1997), we have shown that the matrix representation of Kirchhoo migration operator for homogeneous background in space-frequency domain is a dense matrix, while the compressed beamlet-operator, which is the wavelet decomposition of the Kirchhoo mi...

Let V be an arbitrary system of weights on an open connected subset G of CN (N ≥ 1) and let B (E) be the Banach algebra of all bounded linear operators on a Banach space E. Let HVb (G, E) and HV0 (G, E) be the weighted locally convex spaces of vector-valued analytic functions. In this paper, we characterize self-analytic mappings φ : G → G and operator-valued analytic mappings Ψ : G → B (E) whi...

Wave-equation dip moveout (DMO) addresses the DMO amplitude problem of finding an algorithm which faithfully preserves angular reflectivity while processing data to zero offset. Only three fundamentally different theoretical approaches to the DMO amplitude problem have been proposed: (1) mathematical decomposition of a prestack migration operator; (2) intuitively accounting for specific amplitu...

True amplitude wave equation migration (WEM) provides the quality image of wave equation migration along with proper weighting of the output for estimation of an angularly dependent reflection coefficient, similar to the output of Kirchhoff inversion. In an earlier paper, Zhang et al. (2003) presented a true amplitude WEM for common-shot data in heterogeneous media. Here we present two addition...

Let M be a compact Riemannian manifold with an action by isometries of a compact Lie group G. Suppose that this action could be lifted to an action by isometries on a Clifford bundle E over M. We use the method of the Witten deformation to compute the virtual representation-valued index of a transversally elliptic Dirac operator on E. We express the multiplicities of the associated representati...

Consider the partition function ZQ(a, g) = 1 √ π ∞ −∞TrH(γU(g)ae −Q2+itda)e−t 2 dt. In this paper we give an elementary proof that this is an invariant. This is what we mean: assume that Q is a self-adjoint operator acting on a Hilbert space H, and that the operator Q is odd with respect to a Z2-grading γ of H. Assume that a is an operator that is even with respect to γ and whose square equals ...