The authors prove existence of a stable transfer function satisfying the nonlinear equations characterizing an asymptotic stationary point, in undermodeled cases, for a class of pseudo-linear regression algorithms, including Landau’s algorithm, the Feintuch algorithm, and (S)HARF. The proof applies to all degrees of undermodeling and assumes only that the input power spectral density function i...

In order to get estimates on the solutions of the equation ∂̄u = ω on Stein manifold, we introduce a new method the ”raising steps method”, to get global results from local ones. In particular it allows us to transfer results form open sets in C to open sets in a Stein manifold. Using it we get L − L results for solutions of equation ∂̄u = ω with a gain, s > r, in strictly pseudo convex domains i...

We compute the Szegö kernels of the unit circle bundles of homogeneous negative line bundles over a compact Hermitian symmetric space. We prove that their logarithmic terms vanish in all cases and, further, that the circle bundles are not diffeomorphic to the unit sphere in Cn for Grassmannian manifolds of higher ranks. In particular they provide an infinite family of smoothly bounded strictly ...

This note presents a detailed and self-contained discussion of the Dirichlet problem of real Monge-Ampère equations in strictly convex domains and complex Monge-Ampère equations in strongly pseudo-convex domains. Sections 1.1 and 1.2 follow [2] and [3] respectively, while Sections 2.1, 2.2 and 2.3 are based on [5], [4] and [1] respectively. This note is written for lectures in the Special Lectu...

In this paper an approach to adaptive IIR ltering based on a pseudo-linear regression and a QR matrix decomposition is developed. The algorithm has proved to be stable and has good convergence properties if the unknown system satisses the strictly positive real condition. The derivation of the algorithm is straightforward and the computational complexity is less than the computational complexit...

Suppose we are given an infinite, finitely generated group G and a transient random walk with bounded range on the wreath product (Z/2Z) ≀ G, such that its projection on G is transient. This random walk can be interpreted as a lamplighter random walk, where there is a lamp at each element of G, which can be switched on and off, and a lamplighter walks along G and switches lamps randomly on and ...

In this paper, we introduce regularization methods for finding a point, being not only solution monotone variational inequality problem but also common zero an infinite family of inverse strongly non-self operators closed convex subset in real Hilbert space. these methods, finite number the is used at each iteration step. Applications to fixed point strictly pseudo-contractive and split feasibi...