Generalized Nijenhuis Torsions and Block-Diagonalization of Operator Fields

Diagonalization of Abel's Integral Operator

Courant-Nijenhuis tensors and generalized geometries

Nijenhuis tensors N on Courant algebroids compatible with the pairing are studied. This compatibility condition turns out to be of the form N + N = λI for irreducible Courant algebroids, in particular for the extended tangent bundles T M = TM ⊕ TM . It is proved that compatible Nijenhuis tensors on irreducible Courant algebroids must satisfy quadratic relations N −λN + γI = 0, so that the corre...

Generalized Stationary Random Fields with Linear Regressions - an Operator Approach

Existence, L-stationarity and linearity of conditional expectations E [ Xk ∣. . . , Xk−2, Xk−1 ] of square integrable random sequences X = (Xk)k∈Z satisfying E [ Xk ∣. . . , Xk−2, Xk−1, Xk+1, Xk+2, . . . ] = ∞ ∑ j=1 bj ( Xk−j + Xk+j ) for a real sequence (bn)n∈N, is examined. The analysis is reliant upon the use of Laurent and Toeplitz operator techniques.

Block Diagonalization of Nearly Diagonal Matrices

In this paper we study the effect of block diagonalization of a nearly diagonal matrix by iterating the related Riccati equations. We show that the iteration is fast, if a matrix is diagonally dominant or scaled diagonally dominant and the block partition follows an appropriately defined spectral gap. We also show that both kinds of diagonal dominance are not destroyed after the block diagonali...

Fast block diagonalization of k-tridiagonal matrices

In the present paper, we give a fast algorithm for block diagonalization of k-tridiagonal matrices. The block diagonalization provides us with some useful results: e.g., another derivation of a very recent result on generalized k-Fibonacci numbers in [M.E.A. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456– 4461]; efficient (symbolic) algorithm for...