Perturbations (r τt)t≥0 of the semigroup of shifts (τt)t≥0 on L(R+) are studied under the assumption that r τt−τt belongs to a certain Schatten–von Neumann class Sp with p ≥ 1. It is shown that, for the unitary component in the Wold– Kolmogorov decomposition of the cogenerator of the semigroup (r τt)t≥0, any singular spectral type may be achieved by S1-perturbations. An explicit construction is...

Consider a Hilbert space obtained as the completion of the polynomials C[z ] in m-variables for which the monomials are orthogonal. If the commuting weighted shifts defined by the coordinate functions are essentially normal, then the same is true for their restrictions to invariant subspaces spanned by monomials. This generalizes the result of Arveson [4] in which the Hilbert space is the m-shi...

The semidefinite matrix rank minimization, which has a broad range of applications in system control, statistics, network localization, econometrics and so on, is computationally NPhard in general due to the noncontinuous and non-convex rank function. A natural way to handle this type of problems is to substitute the rank function into some tractable surrogates, most popular ones of which inclu...

Multi-relational learning has received lots of attention from researchers in various research communities. Most existing methods either suffer from superlinear per-iteration cost, or are sensitive to the given ranks. To address both issues, we propose a scalable core tensor trace norm Regularized Orthogonal Iteration Decomposition (ROID) method for full or incomplete tensor analytics, which can...

Let E and P be nonnegative quadratic forms in a Hilbert space H and assume that E + bP is densely defined and closed for every b ≥ 0. For every b > 0 let Hb be the self-adjoint operator associated with E + bP in the sense of Kato’s representation theorem. By Kato’s monotone convergence theorem, the operators (Hb + 1) −1 converge strongly to an operator L, as b tends to infinity. Let k ∈ N. We g...

We define ε-factors in the de Rham setting and calculate the determinant of the Gauß-Manin connection for a family of (affine) curves and a vector bundle equipped with a flat connection. “Ordentliche Leute pflegten ihren Schatten mit sich zu nehmen, wenn sie in die Sonne gingen.” A. v. Chamisso, from ”Peter Schlemihls wundersame Geschichte”