de J Jan Graaf

Singular value decompositions and low rank approximations of multi-linear functionals

The singular value decomposition is among the most important algebraic tools for solving many approximation problems in model reduction, data compression, system identification and signal processing. Nevertheless, there is no straightforward generalization of the algebraic concept of singular values and singular value decompositions to multi-linear functions. Motivated by the problem of finding lower rank approximations of tensors, this paper introduces a notion of singular values for arbitrary multi-linear mappings. An upperbound is derived on the error between a tensor and its optimal lower rank approximation and a conceptual algorithm is proposed to compute singular value decompositions of tensors.

Analyticity spaces of self adjoint operators subjected to perturbations with applications to Hankel invariant distribution spaces

A new theory of generalized functions has been developed by one of the authors (de Graaf). In this theory the analyticity domain of each positive self-adjoint unbounded operator

A measure theoretical Sobolev lemma

\mathcal{A}

A fundamental approach to the generalized eigenvalue problem for self-adjoint operators

in a Hilbert space X is regarded as a test space denoted by

Dual systems of inductive-projective limits of Hilbert spaces originating from self-adjoint operators

\mathcal{S}_{x,\mathcal{A}}

Some maximality results for effect-valued measures

. In the first part of this paper, we consider perturbations

A Characterization of the Spaces

\mathcal{P}

\mathfrak{S}_{{1/{k + 1}}}^{{k /{k + 1}}}

on

by Means of Holomorphic Semigroups

\mathcal{A}

Domains of exponentiated fractional Jacobi operators: Characterizations, classifications, expansion results

for which there exists a Hilbert space Y such that